# Lecture 17. Options trading strategies

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2 I. Basics: One of the attractions of options is that they can be used to create a wide range of different payoff patterns for speculators and hedgers. Basics: Long a call: Time value varies with moneynesses. The longer you hold, the more time value lost. call T 1 T 2 Maturity Long a put put T 1 T 2 Maturity Short a call (put) 2

3 II. Single option and a stock Based on the put-call parity: p + S 0 = c + Ke -rt (p + S 0 D = c + Ke -rt ) +S c p + Ke -rt (long a stock, short a call => short a put, lend Ke -rt at r) profit K +c S p - Ke -rt (long a call, short a stock => long a put, borrow Ke -rt at r) profit K +S + p c - Ke -rt -S - p - c + Ke -rt Stock with dividends Buying a stock at a double discount by selling a put. Selling a stock at a premium by selling a call. 3

4 III. Two options: Different K, the same maturity ~ Call Bull Spreads: Expectation: > S 0 Structure: +C K1 C K2 K 2 > K 1 The same maturity Initial cash flow: Negative. C K2 C K1 Payoff pattern: limit upside return and downside loss. +C K1 C K2 Total (profit) (loss) K 2 - K 1 K 2 - K 2 K 1 K 2 K 1 (C K1 C K2 ) K 2 > > K 1 - K K 1 K 1 (C K1 C K2 ) K (C K1 C K2 ) Maturity T 2 T 1 K 1 K 2 Intuition: The longer (shorter) your hold the bull spread, the higher (lower) the risk. When S is low (high), C K1 (C K2 ) has higher time value. As S is low: at T 1 : at T 2 : Time value of C K1 Time value of C K2 > Time value of C K1 Time value of C K2 As S is high: at T 1 : at T 2 : Time value of C K1 Time value of C K2 < Time value of C K1 Time value of C K2 Both calls are OTM: low cost. It can have profit only when the stock price increases. One call is ITM, the other call is OTM: Both calls are ITM: 4

5 ~ Put Bull Spreads: Expectation: > S 0 Structure: +P K1 P K2 K 2 > K 1 The same maturity Initial cash flow: Positive. +P K2 P K1 Payoff pattern: limit upside return and downside loss. +P K1 P K2 Total (profit) (loss) K P K2 P K1 K 2 > > K 1 0 -K 2 K 2 K 2 + (P K2 P K1 ) K 1 K 1 K 2 K 1 K 2 K 1 K 2 + (P K2 P K1 ) Maturity K 1 K 2 T 2 T1 Intuition: The longer (shorter) your hold the bull spread, the higher (lower) the risk. When S is low (high), P K1 (P K2 ) has higher time value. As S is low: at T 1 : at T 2 : Time value of P K2 Time value of P K1 < Time value of P K2 Time value of P K1 As S is high: at T 1 : at T 2 : Time value of P K2 Time value of P K1 > Time value of P K2 Time value of P K1 Both puts are OTM: low cost. It can have profit only when the stock price increases. One put is ITM, the other put is OTM: Both puts are ITM: 5

6 ~ Call Bear Spreads: Expectation: < S 0 Structure: C K1 + C K2 K 2 > K 1 The same maturity Initial cash flow: Positive. C K1 C K2 Payoff pattern: limit upside return and downside loss. C K1 + C K2 Total K 2 ( - K 1 ) (K 2 - ) (K 2 K 1 ) [K 2 K 1 (C K1 C K2 )] K 2 > > K 1 ( - K 1 ) 0 ( - K 1 ) [ K 1 (C K1 C K2 )] K [ (C K1 C K2 )] ~ Put Bear Spreads: Expectation: < S 0 Structure: P K1 + P K2 K 2 > K 1 The same maturity Initial cash flow: Negative. P K1 P K2 Payoff pattern: limit upside return and downside loss. +P K1 P K2 Total K (P K2 P K1 ) K 2 > > K 1 0 ( -K 2 ) ( K 2 ) [ K 2 + (P K2 P K1 )] K 1 K 1 ( K 2 ) (K 1 K 2 ) [K 1 K 2 + (P K2 P K1 )] 6

7 IV. Three options: Different K, the same maturity Call Butterfly spreads: Expectation: S 0 (volatility is decreasing) Structure: +C K1 2 C K2 + C K3 K 3 > K 2 > K 1 K 2 is closer to S 0 The same maturity Initial cash flow: Negative. 2 C K2 (C K1 + C K3 ) =Initial Payoff pattern: limit return (if the stock price is stable) limit loss (if the stock price is volatile) +C K1 2C K2 +C K3 Total < K Initial K 2 > > K 1 -K K 1 -K 1 + Initial K 3 > > K 2 -K 1-2( -K 2 ) K 1 +2K K 1 +2K 2 +Initial > K 3 -K 1-2( -K 2 ) -K 3 2K 2 -K 1 -K 3 2K 2 -K 1 -K 3 +Initial K 1 K 2 K 3 7

8 ~ Put Butterfly spreads: Expectation: S 0 (volatility is decreasing) Structure: +P K1 2 P K2 + P K3 K 3 > K 2 > K 1 K 2 is closer to S 0 The same maturity Initial cash flow: Negative. 2 P K2 (P K1 + P K3 ) =Initial Payoff pattern: limit return (if the stock price is stable) limit loss (if the stock price is volatile) < K 1 K 2 > > K 1 K 3 > > K 2 > K 3 +P K1 2P K2 +P K3 Total K 1 K 2 K 3 8

10 ~ Put calendar spreads: Expectation: K (volatility is decreasing), trading the time value of options Structure: +P T2 P T1 T 2 > T 1 different Strike price: the same Initial cash flow: Negative. P T1 P T2 =Initial Trading: both options are closed out at T 1 Payoff pattern: limit return (if the stock price close to K) limit loss (if the stock price is volatile) Similar to butterfly spreads P T1 +P T2 Total > K 0 0 (OTM option) Initial < K K- K- + small time value (ITM) Small time value small time value +Initial K high time value high time value big time value +Initial K Reverse put calendar spreads: Diagonal spreads: different K and T. 10

11 IV. Combinations: trade Calls and puts ~ Straddle: Expectation: Structure: Strike price: Initial cash flow: Payoff pattern: << >> K (volatility is increasing), trading the volatility + C + P the same the same Negative. (C + P) = Initial Large return (if the stock price is volatile) limit loss (if the stock price is stable) +C +P Total > K - K 0 - K K (C + P) < K 0 K- K- K- (C + P) K (C + P) K Reverse straddles: 11

12 ~ Strangle: Expectation: <<< > >> K (volatility is increasing a lot), trading the volatility Structure: + C K2 + P K1 K 2 > K 1 (OTM options) the same Strike price: different Initial cash flow: Payoff pattern: Negative. (C K2 + P K1 ) = Initial Large return (if the stock price is volatile) limit loss (if the stock price is stable) + C K2 + P K1 Total > K K 2 0 K 2 K 2 (C K2 + P K1 ) < K 0 K 1 - K 1 - K 1 - (C K2 + P K1 ) K (C K2 + P K1 ) K 1 K 2 Reverse strangles: 12

13 ~ Strips: Expectation: Structure: Strike price: Initial cash flow: Payoff pattern: Volatility is increasing, the stock price is more likely to decrease + C + 2P the same the same Negative. (C + 2P) = Initial Large return (if the stock price is volatile) limit loss (if the stock price is stable) +C +2P Total > K - K 0 - K K (C + 2P) < K 0 2(K- ) 2(K- ) 2(K- ) (C + 2P) K (C + 2P) K Reverse strips: 13

14 ~ Straps: Expectation: Structure: Strike price: Initial cash flow: Payoff pattern: Volatility is increasing, the stock price is more likely to increase + 2C + P the same the same Negative. (2C + P) = Initial Large return (if the stock price is volatile) limit loss (if the stock price is stable) +2C +P Total > K 2( K) 0 2( K) 2( K) (2C + P) < K 0 K- K- K- (2C + P) K (2C + P) K Reverse straps: 14

15 ~ Collars: Expectation: Volatility is decreasing and the stock price is more likely to increase a little. Structure: +S + P K1 C K2 K 2 > K 1 Use the put to hedge downside risk. Use proceeds from call to reduce the cost of hedging. The same maturity Initial cash flow: Negative. ( S + P K1 C K2 ) =Initial Payoff pattern: limit upside return limit down side loss similar to bull spreads +S +P K1 C K2 Total < K 1 K 1-0 K 1 K 1 ( S + P K1 C K2 ) K 2 > > K ( S + P K1 C K2 ) > K 2 0 ( -K 2 ) K 2 K 2 ( S + P K1 C K2 ) K 1 K 2 15

16 ~ Ratio spreads: Expectation: Trade mispriced options. According to the Black-Scholes model, if options are mispriced, we can construct a risk-free portfolio by shorting or longing stocks and other options. In reality, shorting stocks is subjective to the uptick rule. Alternatively, we can use ratio spreads to trade mispriced options. Structure: Buy (sell) undervalued (overvalued) options and sell (buy) correctly priced options. The same maturity Forming a risk-free portfolio: V=N 1 C 1 + N 2 C 2 V= N 1 1 C 1 + N 2 2 C 2 = 0 N N 1 2 N1 = N2 ( ) 1 16

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