FINANCIAL ENGINEERING CLUB TRADING 201

FINANCIAL ENGINEERING CLUB TRADING 201

GREG PASTOREK

OPTIONS REVIEW A call (put) option with strike K expiring on date T gives the owner the right to buy (sell) the underlying security for price K until date T. For stock options, 1 option gives the right to buy/sell 100 stock.

OPTIONS PRICING In order to trade options, we need to understand how they are priced The Black-Scholes equation calculates the price of an option based on a number of variables including: Stock Price Strike Time to Expiration Interest Rates Volatility

OPTION PRICING It s all about volatility Volatility is the measure of how much a stock moves, the true future volatility is unknown. The implied volatility (IV) of a stock is the price volatility implied from the options prices For each day into the future, we can forecast a probability distribution for a stock price

STOCK PRICE The change in the option price as a function of the change in the stock price is known as Delta Delta is the first derivative with respect to stock price of the Black-Scholes option pricing equation

STOCK PRICE Delta can be viewed as the probability of an option expiring ITM Far ITM options have ±100 deltas ATM options have ±50 deltas Far OTM options have 0 deltas

STOCK PRICE Gamma is the second derivative with respect to stock price of the Black-Scholes equation So Delta tells you how much the option price will change if the stock price increases by $1, c.p. Gamma tells you how Delta changes if the stock price increases by $1, c.p. Gamma is highest for ATM options

STOCK PRICE Note that a long gamma position favors price movement while a short gamma position favors little to no price movement If we are long gamma, the stock price increases, then our delta exposure will increase. We become increasingly long delta as the price increases

HEDGING WITH DELTA Hedging is the idea of reducing risk By hedging a trade, we are limiting the profitability of a trade while at the same time decreasing the amount of risk we are taking Suppose we are trading options, and we do not want to make any bets on the underlying price movement, then we would want to hedge against the underlying price risk.

HEDGING WITH DELTA So for example, if we sold an OTM Call in some underlying then we are short Deltas A hedge would be any trade that adds long Deltas in the same underlying so that we are (near) zero deltas. This could include buying the underlying, buying a Call at a different strike, selling a Put, etc.

HEDGING WITH DELTA Also note that delta hedging doesn t protect against large underlying changes because of gamma Your delta changes as price changes too!

TIME TO EXPIRATION Theta is the first derivative with respect to time of the Black- Scholes options pricing equation Options decrease in price over time Theta will always be given as a negative value equal to the decrease in an options price given 1 day has passed, c.p. Refer to theta position as paying theta and collecting theta.

TIME TO EXPIRATION If options have a lot of time till their expiration, they have a greater chance of winding up ITM If there is only 1 day left until expiration, an OTM option will be much cheaper than an option at the same strike if there were 100 days until expiration, c.p. OTM options will be worthless at expiration ITM options will converge to their intrinsic value

TIME TO EXPIRATION ATM options are more sensitive to time than deep ITM or far OTM options All long option position will pay Theta. A long (short) gamma position will always pay (collect) Theta.

VOLATILITY Vega is the first derivative with respect to volatility of the Black-Scholes options pricing equation Volatility makes options more expensive If you have limited loss and unlimited profit potential, more volatility will increase the expected profit of a long position.

VOLATILITY Options traders are generally trading volatility and vega is their unit of risk since delta is generally hedged Gamma and theta are closely tied with some exceptions (time-spreads) Volatility is a mean-reverting process Implied vs. Realized Volatility

VOLATILITY ATM options are more sensitive to changes in volatility than deep ITM or far OTM options Vega is highest for ATM options All options have positive Vega

SKEW Volatility skew describes how volatility risk (vega) varies from low to high strikes High skew positions are at risk of reaching large vega for large (one direction) moves in the underlying

SKEW For example, risk reversal:

KURTOSIS Volatility kurtosis describes how volatility risk (vega) varies from ITM/OTM strikes to ATM strikes High kurtosis positions are at risk of reaching large vega for large (either direction) moves in the underlying

KURTOSIS For example, iron condor:

INTEREST RATES Rho is the first derivative with respect to the risk-free rate of interest of the Black-Scholes equation Rho tells you how much an option price will change with a 1 percentage-point increase in interest rates Rho is positive for Calls and negative for Puts

THE GREEKS Delta, Gamma, Vega, Theta, and Rho are collectively known as the Greeks They are various derivatives of the Black-Scholes options pricing equation

PROBLEMS The Black-Scholes model does not agree with reality in a number of ways Assumes stock returns are log-normally distributed, ignores the fat tails that account for black swan events Black-Scholes is also used to price European options while we will typically be dealing with American options Assumes volatility is constant across all strikes, in reality we see a skew or a smile. No transactions costs, unlimited short selling, etc.

SYNTHETICS Long Call + Short Put = Long 1 Underlying Short Call + Long Put = Short 1 Underlying Try to find arbitrage relationships! Account for interest. Long 1 call + Short 1 Put is equivalent to holding 100 shares of stock, but you pay less cash to hold the option position so you have more capital to earn interest on

PUT-CALL PARITY For European Options For American Options C P = S Ke rt S K C P S Ke rt Using Put-Call Parity, traders can quickly identify mispricings by relative value

BOX SPREAD Long (lower) Call Short (higher) Call Long (higher) Put Short (lower) Put Selling box spreads is similar to taking a loan at the risk free rate

PIN RISK Scenario: You are short a call or put option and the option expires ATM. You don t know if the option was used until the next day, so you are unsure how to hedge your delta overnight Can turn a box spread into a high delta position! Avoid PIN risk by avoiding holding ATM options near expiration

NICK GARFIELD

OPPORTUNITIES We re going to look for places where the market gives us an edge (mispricings) We re going to look for reversion to the mean We re going to trade with probabilities, not emotions

SELLING THETA All option prices decrease over time, c.p. Buying a Call or a Put has the disadvantage of time decay We can take advantage of theta by short-selling options

SELLING THETA Selling theta is the strategy of selling OTM Calls and Puts instead of buying them By selling options, we take advantage of the theta decay in their prices Studies have shown that the fastest rate of Theta decay occurs while options are in the 45-15 DTE range So, looking to selling options with 45 DTE should provide you with a slight edge

VOLATILITY MEAN REVERSION Volatility is a highly mean-reverting statistic We can take advantage of this by selling options with volatile underlyings Selling options in a volatile stock not only gives you a greater POP but also more profit Options are more expensive in a volatile underlying. By selling them, we take in a greater max profit

USE THE PROBABILITIES Find a percentage that is comfortable for your trading Selling an option with a strike 1 SD away from the current price has a POP of around 82% Selling an option with a strike 2 SD away form the current price has a POP of around 98% POP is the probability of making at least $0.01 on a trade If we are selling options, POP is the probability that the stock will not be beyond the option s strike at expiration

USE THE PROBABILITIES

POP OF 1 SD SHORT CALL

POP 2 SD SHORT CALL

USE THE PROBABILITIES Probability ITM is the probability that an option will expire in the money Probability of a touch (POT) is the probability that we will be tested at some point during our trade It is the probability that the stock will touch our short strike point sometime between now and our option s expiration date POT = 2 Prob. ITM So the 1 SD short option will be tested approximately 36% of the time

SPREADS A spread is the simultaneous trade of two or more options Verticals Strangles Iron Condors

VERTICALS A Vertical is made up of a short option and a long option at different strike prices with the same expiration This is risk-defined trade to use when you have a directional assumption about a particular stock The max loss for a short vertical is equal to the width of the strikes minus the credit received The max loss for a long vertical is equal to the debit paid for the position

VERTICALS Trade short verticals when there is relatively high IV and we are looking for a volatility contraction Trade long verticals when there is relatively low IV and we are looking for a volatility expansion

VERTICALS Verticals can be thought of as a hedge to the naked option position We are combining two positions of both long and short Deltas into the same underlying Decreases our POP but also defines our max loss

SHORT VERTICALS Sell an OTM strike Buy a further OTM strike Credit received is the difference between the two prices

SHORT CALL VERTICALS Your max loss is the difference between the strikes minus the credit received Your max profit is the total credit you received for selling the spread

LONG CALL VERTICALS Your max loss of buying a Long Vertical is the total premium you paid for the position Your max profit is difference between the strikes minus the premium paid

VERTICALS EXAMPLE Long AAPL Sept 50 Call for $2.00 Short APPL Sept 60 Call for $0.75 Total Cost? Max Loss? Max Profit?

STRANGLES A strangle is a position that consists of selling both a short Call and a short Put The strategy is profitable when the underlying stays above the strike of the short put and below the strike of the short call The trade will lose money when the underlying moves outside of this defined range Excellent strategy to employ with high IV

STRANGLES Sell an OTM Put Sell an OTM Call Credit received is the sum of the two prices

STRANGLES Your max loss is infinite Your max profit is the total credit you received for selling the strangle

STRANGLES

IRON CONDORS The Iron Condor is a mix of the short vertical and the strangle It is a position consisting of the selling a short Call spread and selling a short Put spread Unlike the strangle, the icon condor has a defined max loss and a lower POP Like the strangle, the iron condor is profitable when he underlying stays between the two strikes

IRON CONDORS Sell an OTM Put vertical Sell an OTM Call vertical Credit received is the sum of the two sales

IRON CONDORS Your max loss is limited and defined unlike the strangle Your max profit is the total credit you received for selling the spread

SPREADS Short verticals, strangles, and iron condors all of the the advantage of theta decay They tend to work best in high-vol environments and take advantage of volatility s reversion to the mean Easy to understand and calculate the POP

Time Spreads Short front-month ATM straddle Long back-month ATM straddle Short gamma (since the front-month gamma explodes as expiration approaches) Short gamma = Collecting theta We are long vega, front month vega is less than back month. We have gamma and vega opposite signs!

BREAK-EVENS Short Call Verticals: Short Strike + Credit Received Short Put Verticals: Short Strike Credit Received Strangles: Call side: Short Strike + Credit Received Put side: Short Strike Credit Received Iron Condors: Same as above

CLOSING TRADES We can significantly improve our POP by locking in profits and taking off trades at 50% of max profit For example, if we sell a short Put vertical for $2.00, the probability that the vertical will trade for $1.00 sometime between now and expiration is significantly greater than the probability than the short Put vertical will expire worthless So if we lock in profits at 50%, we can take some risk off the table and move on to the next trade

THANK YOU