# FINANCIAL ENGINEERING CLUB TRADING 201

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1 FINANCIAL ENGINEERING CLUB TRADING 201

2 STOCK PRICING It s all about volatility Volatility is the measure of how much a stock moves The implied volatility (IV) of a stock represents a 1 standard deviation (SD) range of where the stock might be in 1 year For each day into the future, we can forecast a probability distribution for a stock price

3 STOCK PRICING A stock will be within a 1 SD move 68% of the time A stock will be within a 2 SD move 95% of the time For example, if AAPL stock is at \$100 with an IV of 20%, then one year from today, AAPL would have a 68% chance of being within \$80 and \$120 AAPL stock would have a 95% chance of being within \$60 and \$140 one year from today

4 STOCK PRICING We can calculate this probability curve for individual days in the future The standard deviation of that curve for t days into the future is given by the following expression:

5 NOTES Our model for future stock price movements is probabilistic and normal distributed This model doesn t look at balance sheets, trends, chart patterns, P/E ratios, etc. In our model, a stock price has a chance of moving either up or down In reality, there s a slight upwards drift

6 WHAT DOES THIS MEAN? Calculate a probability of profit (POP) for our positions Calculate a probability of touch (POT) for an option Provide realistic expectations for future price movements

7 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 Volatility Time to Expiration Interest Rates

8 STOCK PRICE Last time we looked at the concepts of ITM and OTM options ITM options are worth more than OTM options

9 STOCK PRICE So, say I short sell an OTM Call. Now the stock price moves such that the call moves further OTM. With all other things being held equal (c.p.), the price of the Call will have decreased We could then buy back this Call for a profit on the difference between our sell price and our buy price If I were to have bought this same Call, I would be at a loss equal to the difference between my buy price and the current stock price

10 STOCK PRICE Calls get more expensive when the stock moves up Puts get more expensive when the stock moves down c.p.

11 STOCK PRICE This 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

12 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.

13 VOLATILITY Vega is the first derivative with respect to volatility of the Black-Scholes options pricing equation Volatility makes options more expensive

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

15 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.

16 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

17 TIME TO EXPIRATION ATM options are more sensitive to time than deep ITM or far OTM options All options have negative Theta

18 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

19 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

20 HOW DO I MAKE MONEY? We re going to look for places where the market gives us an advantage We re going to look for reversion to the mean We re going to trade with probabilities, not emotions

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

22 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 DTE range So, looking to selling options with 45 DTE should provide you with a slight edge

23 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

24 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

25 USE THE PROBABILITIES

26 POP OF 1 SD SHORT CALL

27 POP 2 SD SHORT CALL

28 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

29 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 Generally, we should hedge when our initial assumptions on the underlying have changed. A hedge is a trade that will profit if our initial position is violated even further

30 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 This could include buying the underlying, buying a Call at a different strike, selling a Put, etc.

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

32 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

33 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

34 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

35 Calls Strike Puts SHORT VERTICALS \$ \$2.00 \$ \$2.40 Sell an OTM strike Buy a further OTM strike Credit received is the difference between the two prices \$ \$2.70 \$ \$2.90 \$ \$3.00 \$ \$3.20 \$ \$3.50 \$ \$4.00 \$ \$5.50

36 LONG CALL VERTICALS \$5 \$3 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 \$2 \$0 -\$2 -\$3 -\$

37 SHORT CALL VERTICALS \$5 \$3 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 \$2 \$0 -\$2 -\$3 -\$

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

39 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

40 Calls Strike Puts STRANGLES \$ \$2.00 \$ \$2.40 \$ \$2.70 Sell an OTM Put Sell an OTM Call Credit received is the sum of the two prices \$ \$2.90 \$ \$3.00 \$ \$3.20 \$ \$3.50 \$ \$4.00 \$ \$5.50

41 STRANGLES \$5 \$3 \$2 Your max loss is infinite Your max profit is the total credit you received for selling the strangle \$0 -\$2 -\$3 -\$

42 STRANGLES

43 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

44 Calls Strike Puts IRON CONDORS \$ \$1.96 \$ \$2.23 Sell an OTM Put vertical Sell an OTM Call vertical Credit received is the sum of the two sales \$ \$2.52 \$ \$2.86 \$ \$3.24 \$ \$6.15 \$ \$10.56 \$ \$15.49 \$ \$20.49

45 Calls Strike Puts IRON CONDORS \$ \$2.00 \$ \$2.40 Sell an OTM Put vertical Sell an OTM Call vertical Credit received is the sum of the two sales \$ \$2.70 \$ \$2.90 \$ \$3.00 \$ \$3.20 \$ \$3.50 \$ \$4.00 \$ \$5.50

46 IRON CONDORS \$5 \$3 \$2 Your max loss is defined as the Your max profit is the total credit you received for selling the strangle \$0 -\$2 -\$3 -\$

47 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

48 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

49 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

50 THANK YOU

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