Equity hybrid derivatives pdf

It has proved over time to be the most flexible, intuitive and popular approach to option pricing. It is one of the most popular, relative simple and fast modes of calculation. Unlike the binomial model, it does not rely on calculation by iteration. This measures the sensitivity of the option value to a given small change in the price of the underlying asset. It may also be seen as the speed with which an option moves with respect to price of the underlying asset.

Delta for call option buyer is positive. This means that the value of the contract increases as the share price rises. Delta for call option seller will be same in magnitude but with the opposite sign negative. The value of the contract increases as the share price falls. Delta for put option seller will be same in magnitude but with the opposite sign positive.

Therefore, delta is the degree to which an option price will move given a change in the underlying stock or index price, all else being equal. The knowledge of delta is of vital importance for option traders because this parameter is heavily used in margining and risk management strategies. The delta is often called the hedge ratio, e. This is called a second derivative option with regard to price of the underlying asset.

It is calculated as the ratio of change in delta for a unit change in market price of the underlying asset. Theta is the change in option price given a one-day decrease in time to expiration. It is a measure of time decay.

Theta is generally used to gain an idea of how time decay is affecting your option positions. Other things being equal, options tend to lose time value each day throughout their life. This is due to the fact that the uncertainty element in the price decreases. An increase in the assumed volatility of the underlying increases the expected payout from a buy option, whether it is a call or a put. Among other things, a trader must also consider the premium of these three options in order to make an educated decision.

As discussed earlier there are two components in the option premium — intrinsic value and time value. In case of at-the-money or out-of-the-money options there is no intrinsic value but only time value. Hence, these options remain cheaper compared to in-the-money options. Therefore, option buyer pays higher premium for in-the-money option compared to at-the-money or out-of-the-money options and thus, the cost factor largely influences the decision of an option buyer.

Let us consider call options with strike prices of , , and A call option buyer will buy the option and pay the premium upfront. The premiums for various strike prices are as follows: Strike Price Premium Hence the option premium will always be at least equal to this value.

The remaining portion of the premium is the time value There is no intrinsic value here. The entire option premium is attributed to risk associated with time, i. The greatest loss will be for option with strike price Rs. The choice of option would be better understood with return on investment ROI.

In each case, ROI is defined as net profit as a percentage of premium paid by the option buyer. Pay offs for call options with different strikes and premiums X Nifty Closing P A person bearish on the Nifty can buy a put option of any strike available. The premiums for each of these are given below: Strike Price Premium 69 98 In case of the strike option, the intrinsic value is — For the other two options, the entire premium is the time value Pay offs for put options with different strikes and premiums X Nifty Closing P 69 98 Similarly strike price is out of the money and so the contract is selling at low premium of Rs.

In terms of return on investment criterion, buyer of deep out of the money option will gain the maximum return, if price of the Nifty falls drastically. On the other hand, selling deep out of the money put options is less risky but they come with low premium.

Depending upon his analysis of the then existing market conditions and his risk appetite, he can devise various strategies, which we will see in the next chapter. As long as the trader can think of innovative combinations of various options, newer strategies will keep coming to the market. In this section, we will see some of the most commonly used strategies.

These are limited profit and limited loss positions. Further, these can be created either using calls as combination or puts as combination. So he takes one long call position with lower strike and sells a call option with higher strike. As lower strike call will cost more than the premium earned by selling a higher strike call, although the cost of position reduces, the position is still a net cash outflow position to begin with.

Secondly, as higher strike call is shorted, all gains on long call beyond the strike price of short call would get negated by losses of the short call.

To take more profits from his long call, trader can short as high strike call as possible, but this will result in his cost coming down only marginally, as higher strike call will fetch lesser and lesser premium. Say, for example, a trader is bullish on market, so he decides to go long on strike call option by paying a premium of and he expects market to go not above , so he shorts a call option and receives a premium of Long Call Short Call Net Flow As can be seen from the above pay off chart, it is a limited profit and limited loss position.

Maximum profit in this position is and maximum loss is BEP for this spread is Bullish Vertical Spread using Puts Here again, the call on the market is bullish, hence, the trader would like to short a put option.

If prices go up, trader would end up with the premium on sold puts. However, in case prices go down, the trader would be facing risk of unlimited losses. In order to put a floor to his downside, he may buy a put option with a lower strike.

While this would reduce his overall upfront premium, benefit would be the embedded insurance against unlimited potential loss on short put.

This is a net premium receipt strategy. Short Put Long Put Net Flow As can be seen from the picture above, it is a limited profit and limited loss position. Maximum profit in this position is 50 and maximum loss is BEP for this position is The risk in a naked short call is that if prices rise, losses could be unlimited. So, to prevent his unlimited losses, he longs a high strike call and pays a lesser premium. Thus in this strategy, he starts with a net inflow. Long Call Short Call Net Flow As can be seen from the picture above, it is a limited profit and limited loss position.

Bearish Vertical Spread using puts Here, again the trader is bearish on the market and so goes long in one put option by paying a premium.

Further, to reduce his cost, he shorts another low strike put and receives a premium. This is also known as time spread or calendar spread.

Here, it is not possible to draw the pay off chart as the expiries underlying the spread are different. Underlying reasoning behind horizontal spreads is that these two options would have different time values and the trader believes that difference between the time values of these two options would shrink or widen. This is essentially a play on premium difference between two options prices squeezing or widening.

Diagonal spread Diagonal spread involves combination of options having same underlying but different expiries as well as different strikes. Again, as the two legs in a spread are in different maturities, it is not possible to draw pay offs here as well.

These are much more complicated in nature and in execution. These strategies are more suitable for the OTC market than for the exchange traded markets. A long straddle position is created by buying a call and a put option of same strike and same expiry whereas a short straddle is created by shorting a call and a put option of same strike and same expiry.

Let us say a stock is trading at Rs. Long Straddle If a person buys both a call and a put at these prices, then his maximum loss will be equal to the sum of these two premiums paid, which is equal to And, price movement from here in either direction would first result in that person recovering his premium and then making profit.

Now, let us analyze his position on various market moves. Let us say the stock price falls to at expiry. Now, consider that the stock price shoots up to Thus, it can be seen that for huge swings in either direction the strategy yields profits.

However, there would be a band within which the position would result into losses. Further, as long as underlying expires between and , he would always incur the loss and that would depend on the level of underlying. His profit would start only after recovery of his total premium of Rs. Short Straddle This would be the exact opposite of long straddle.

So, he sells a call and a put so that he can profit from the premiums. As position of short straddle is just opposite of long straddle, the pay off chart would be just inverted, so what was loss for long straddle would become profit for short straddle. Short Call Short Put Net Flow It should be clear that this strategy is limited profit and unlimited loss strategy and should be undertaken with significant care. Further, it would incur the loss for trader if market moves significantly in either direction — up or down.

Long Strangle As in case of straddle, the outlook here for the long strangle position is that the market will move substantially in either direction, but while in straddle, both options have same strike price, in case of a strangle, the strikes are different. Also, both the options call and put in this case are out-of-the-money and hence the premium paid is low.

Let us say the cash market price of a stock is Both these options are out-of-the-money. If a trader goes long on both these options, then his maximum cost would be equal to the sum of the premiums of both these options. This would also be his maximum loss in worst case situation. However, if market starts moving in either direction, his loss would remain same for some time and then reduce.

And, beyond a point BEP in either direction, he would make money. Let us see this with various price points. If spot price falls to on maturity, his long put would make profits while his long call option would expire worthless.

In case stock price goes to at expiry, long call would become profitable and long put would expire worthless. Long Call Long Put Net Flow In this position, maximum profit for the trader would be unlimited in both the directions — up or down and maximum loss would be limited to Rs. Position would have two BEPs at and Until underlying crosses either of these prices, trader would always incur loss. Outlook, like short straddle, is that market will remain stable over the life of options.

Pay offs for this position will be exactly opposite to that of a long strangle position. As always, the short position will make money, when the long position is in loss and vice versa. Short Call Short Put Net Flow In this position, maximum loss for the trader would be unlimited in both the directions — up or down and maximum profit would be limited to Rs.

Until underlying crosses either of these prices, trader would always make profit. If an investor has bought shares and intends to hold them for some time, then he would like to earn some income on that asset, without selling it, thereby reducing his cost of acquisition. So how does an investor continue to hold on to the stock, earn income and reduce acquisition cost? Lets us see: Suppose an investor buys a stock in the cash market at Rs.

If the stock price moves up from level, he makes profit in the cash market but starts losing in the option trade. This is called synthetic short put position. If at that point of time, a strike put is available at any price other than Rs. Indeed, one needs to also provide for frictions in the market like brokerage, taxes, administrative costs, funding costs etc. The most important factor in this strategy is the strike of the sold call option.

If strike is close to the prevailing price of underlying stock, it would fetch higher premium upfront but would lock the potential gain from the stock early. And, if strike is too far from the current price of underlying, while it would fetch low upfront premium, would provide for longer ride of money on underlying stock. A simple perspective on strike choice for covered call is that, till the time the cash market price does not reach the pre determined exit price, the long cash position can be used to sell calls of that target strike price.

The moment is reached in the spot market, we can sell in the cash market and also cover the short call position. A mutual fund manager, who is anticipating a fall, can either sell his entire portfolio or short futures to hedge his portfolio. In both cases, he is out of the market, as far as profits from upside are concerned.

What can be done to remain in the market, reduce losses but gain from the upside? Buy insurance! By buying put options, the fund manager is effectively taking a bearish view on the market and if his view turns right, he will make profits on long put, which will be useful to negate the MTM losses in the cash market portfolio. Let us say an investor buys a stock in the cash market at and at the same time buys a put option with strike of by paying a premium of Rs.

This is called synthetic long call position. Readers may recall that in case of covered call, the downside risk remains for falling prices; i. In our example, we had assumed that a trader longs a stock and shorts a call option with a strike price of and receives Rs.

If price fell below , loss could be unlimited whereas if price rose above , the profit was capped at Rs. To prevent the downside, let us say, we now buy an out-of-the-money put option of strike by paying a small premium of Rs. Net Long Stock Short Call Long Put It is important to note here is that while the long put helps in reducing the downside risk, it also reduces the maximum profit, which a covered call would have generated.

Also, the BEP has moved higher by the amount of premium paid for buying the out-of- the-money put option. We may recollect that downside in short straddle is unlimited if market moves significantly in either direction.

To put a limit to this downside, along with short straddle, trader buys one out of the money call and one out of the money put. Butterfly spread can be created with only calls, only puts or combinations of both calls and puts. Here, we are creating this position with help of only calls. To do so, trader has to take following positions in three different strikes and same maturity options: Long Call 1 with strike of and premium paid Rs.

Both the shorted calls earn the premium for the trader. This entire premium is kept by the trader for all prices less than or equal to And, total of all 4 would always be equal to — To create this position from puts, one needs to buy one highest strike option, sell two middle strike options and then again buy one lowest strike option.

And, to create this position from combination of calls and puts, one need to buy one call at lowest strike, sell one call at middle strike, buy one put at highest strike and sell one put at middle strike. This is limited profit and limited loss strategy. However, the best way to develop an understanding of the trading system is to actually watch the screen and observe trading.

As stated earlier, futures and options are standardized contracts and like shares, they are traded on exchanges. Open outcry is the way of communication between professionals on an exchange, which involves shouting, or using hand signals to transfer information about buy and sell orders.

Thus, such a market brings together the buyers and sellers through their brokers on a platform for trading. In case of electronic trading, there are screen based broker dealing terminals, instead of the trading pit. Futures and options trading in India is electronic in nature, with the bids and offers, and the acceptance being displayed on the terminal continuously.

These trading systems support an order driven market and simultaneously provide complete transparency of trading operations. Derivative trading is similar to that of trading of equities in the cash market segment.

They can trade either on behalf of their clients or on their own account. The exchange assigns a trading member ID to each of its trading member. A trading member can have more than one user. The number of users allowed for each trading member is decided by the exchange from time to time. A user must be registered with the exchange where he is assigned a unique user ID. The unique trading member ID is common for all the users of a particular trading member.

PCM is not a Trading Member of the exchange. Such CMs may clear and settle only their own proprietary trades and their clients' trades but cannot clear and settle trades of other TM's.

Participants: Participant is a client of a trading member. Clients may trade through various trading members but settle through a single clearing member. Market Timing of Derivative segment Trading on the derivatives segment takes place on all working days of the week between am and pm.

Corporate Hierarchy In the Futures and options trading software, trading member will have a provision of defining the hierarchy amongst users of the system. Corporate Manager can perform all the functions such as order and trade related activities, receiving reports for all branches of the trading member firm and also all dealers of the firm.

Along with this he can also define exposure limits for the branches of the firm. This facility is available only to the corporate manager. Branch Manager: As a user, it is placed under the corporate manager.

Branch Manager can perform and view order and trade related activities for all dealers under that branch. Dealer: Dealer is at the lowest level of the user hierarchy.

He can only view his own orders and trades and does not have access to information on other dealers under either the same branch or in other branches. Order types and conditions In the trading system, trading members are allowed to enter orders with various conditions attached to them as per their requirements.

Time conditions Day order: A Day order is an order which is valid for a single day on which it is entered. If the order is not executed during the day, the trading system cancels the order automatically at the end of the day. An unmatched order will be immediately cancelled. Partial order match is possible in this order, and the unmatched portion of the order is cancelled immediately.

Price condition Limit order: It is an order to buy or sell a contract at a specified price. The user has to specify this limit price while placing the order and the order gets executed only at this specified limit price or at a better price than that lower in case of buy order and higher in case of a sell order. Price is not specified at the time of placing this order.

The price will be the currently available price in the market i. Stop-loss order: A stop loss is an order to buy or sell a security once the price of the security climbed above or dropped below a trigger price. To illustrate, suppose a trader buys ABC Ltd. However, prices starts declining below his buy price, trader would like to limit his losses.

Trader may place a limit sell order specifying a trigger price of Rs 95 and a limit price of Rs Once the market price of ABC breaches the trigger price i.

Rs 95, the order gets converted to a limit sell order at Rs Trigger Price is the price at which the order gets triggered from the stop loss book. Orders, as and when they are received, are first time stamped and then immediately processed for potential match.

If a match is not found, then the orders are stored in different 'books'. The best buy order will match with the best sell order.

An order may match partially with another order resulting in multiple trades. For order matching, the best buy order is the one with highest price and the best sell order is the one with lowest price. This is because the computer views all buy orders available from the point of view of a seller and all sell orders from the point of view of the buyers in the market.

Price Band There are no price bands applicable in the derivatives segment. In view of this, orders placed at prices which are beyond the operating ranges would reach the Exchange as a price freeze. Client account number should be provided for client orders. New contract is introduced Trading Cycle on the next trading day following the expiry of near month contract. Last Thursday of the expiry month. If expiry day is Date a holiday, then the immediately preceding business day.

Delivery Based Settlement. On the last trading day, the closing Final Settlement value of the underlying stock is the final settlement price of the expiring futures contract. New contract is Trading Cycle introduced on the next trading day following the expiry of near month contract. Closing price of such underlying security on the last trading Final Settlement Price day of the options contract. Settlement Style Delivery based For further details on product specifications, please refer to the following websites of exchanges: www.

Eligibility criteria of stocks A stock on which stock option and single stock futures contracts are proposed to be introduced shall conform to the following broad eligibility criteria: a The stock shall be chosen from amongst the top stocks in terms of average daily market capitalization and average daily traded value in the previous six months on a rolling basis. For this purpose, a stocks quarter-sigma order size shall mean the order size in value terms required to cause a change in the stock price equal to one-quarter of a standard deviation.

The market wide position limit number of shares shall be valued taking the closing prices of stocks in the underlying cash market on the date of expiry of contract in the month. If a stock fails to meet these retention criteria for three months consecutively, then no fresh month contract shall be issued on that stock. However, the existing unexpired contracts may be permitted to trade till expiry and new strikes may also be introduced in the existing contract months.

Re-introduction of dropped stocks A stock which is dropped from derivatives trading may become eligible once again. In such instances, the stock is required to fulfil the eligibility criteria for three consecutive months to be re-introduced for derivatives trading.

Derivative contracts on such stocks may be re-introduced by the exchange subject to SEBI approval. The index on which futures and options contracts are permitted shall be required to comply with the eligibility criteria on a continuous basis.

The Exchange shall check whether the index continues to meet the aforesaid eligibility criteria on a monthly basis.

If the index fails to meet the eligibility criteria for three consecutive months, then no fresh contract shall be issued on that index. However, the existing unexpired contracts shall be permitted to trade till expiry and new strikes may also be introduced in the existing contracts.

The basis for any adjustment for corporate action shall be such that the value of the position of the market participants on cum and ex-date for corporate action shall continue to remain the same as far as possible. This will facilitate in retaining the relative status of positions viz. This will also address issues related to exercise and assignments. The adjustments for corporate actions shall be carried out on all open positions. Position: The new position shall be arrived at by multiplying the old position by the adjustment factor as under.

However, in cases where the announcement of dividend is made after the close of market hours, the same day's closing price would be taken as the market price. Further, if the shareholders of the company in the AGM change the rate of dividend declared by the Board of Directors, then to decide whether the dividend is extra-ordinary or not would be based on the rate of dividend communicated to the exchange after AGM and the closing price of the stock on the day previous to the date of the AGM.

The basis for any adjustment for corporate actions shall be such that the value of the position of the market participants, on the cum- and ex-dates for the corporate action, shall continue to remain the same as far as possible. This limit contracts. This limit would be applicable on aggregate open positions in all futures and all option contracts on a particular underlying stock.

They publish all or some of the following details for the derivatives contracts being traded on the exchanges. Date: This gives the Trade date. Symbol: This gives the underlying index or stock e. Instrument: This gives the contract descriptor for the various instruments available in the derivatives segment e. Expiry date: The date on which the contract expires Option Type: This gives the type of option for the contract.

This flag changes when there is a corporate action on a contract, which could either be a symbol change or a dividend announced by the company. Strike Price: This gives the Strike Price of the contract. Opening price: This gives the price at which the contract opened for the day.

High price: This gives the highest price at which the contract was traded during the day. Low price: This gives the lowest price at which the contract was traded during the day. Closing price: This gives the price of the contract at the end of the day. Last traded price: This gives the price at which the last contract of the day was traded. Open Interest: For futures contracts open interest is equivalent to the open positions in that futures contract multiplied by its last available closing price.

For option contracts, open interest is equivalent to the open positions multiplied by the notional value. Notional value with respect to an option contract is computed as the product of the open position in that option contract multiplied by the last available closing price of the underlying.

Total Traded Quantity: This is the total no. Download or read book entitled Equity Derivatives and Hybrids written by Oliver Brockhaus and published by Springer online.

This book was released on 29 April with total page pages. Book excerpt: Since the development of the Black-Scholes model, research on equity derivatives has evolved rapidly to the point where it is now difficult to cut through the myriad of literature to find relevant material. Written by perhaps the finest quant shop in the world, this book presents the state of the art in modeling equity hybrid derivatives. This guide is a practical reference and a great complement to anybodys financial library.

By discussing exotic options and hybrids in a practical, non-mathematical and highly intuitive setting, this book will blast through the misunderstanding of exotic derivatives, enabling practitioners to fully understand and correctly This book provides a hands-on guide to how financial models are actually implemented and used in practice, on a daily basis, for pricing and risk-management purposes.

A succinct book that provides readers with all they need to know about the equity derivatives business. Hybrids have a hybrid nature containing different income types or elements of both equity and debt instruments.

Skip to content. Citation Type. Has PDF. Publication Type. More Filters. This … Expand. Pricing long-maturity equity and FX derivatives with stochastic interest rates and stochastic equity. We allow all driving model factors to be instantaneously correlated with each … Expand. Furthermore we allow all driving model factors to be instantaneously … Expand. View 2 excerpts, references methods. Substantial progress has been made in extending the Black-Scholes model to incorporate such features as stochastic volatility, stochastic interest rates and jumps.

On the empirical front, however, it … Expand.