8/3/2019 Derivative Option Strategies_Lecture
1/18
Options Trading Strategies
Liuren Wu
Zicklin School of Business, Baruch College
Options Markets
(Hull chapter: 10)
Liuren Wu (Baruch) Options Trading Strategies Options Markets 1 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
2/18
Objectives
A strategy is a set of options positions to achieve a particular risk/returnprofile.
For simplicity, we focus on strategies that involve positions in only Europeanoptions on the same underlying and at the same expiration.
The zero-coupon bond and the underlying forward of the same maturity arealways assumed available.
We hope to achieve three objectives:1 Given a strategy (a list of derivative positions), we can figure out its
risk profile, i.e., the payoff of the strategy at expiry under differentmarket conditions (different underlying security price levels).
2 Given a targeted risk profile at a certain maturity (i.e., a certain payoffstructure), we can design a strategy using bonds, forwards, and optionsto achieve this profile.
3 Be familiar with (the risk profile, the objective, and the compositionof) the most commonly used, simple option strategies, e.g., straddles,strangles, butterfly spreads, risk reversals, bull/bear spreads.
Liuren Wu (Baruch) Options Trading Strategies Options Markets 2 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
3/18
Put-call conversionsPlot the payoff function of the following combinations of calls/puts and forwardsat the same strike K and maturity T.
1
Long a call, short a forward. Compare the payoff to long a put.
2 Short a call, long a forward.
Compare the payoff to short a put.
3 Long a put, long a forward.
Compare the payoff to long a call.
4 Short a put, short a forward.
Compare the payoff to short a call.
5 Long a call, short a put.
Compare the payoff to long a forward.
6 Short a call, long a put.
Compare the payoff to short a forward.
Liuren Wu (Baruch) Options Trading Strategies Options Markets 3 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
4/18
Put-call conversions: Payoff comparison (K = 100)1 2 3
80 85 90 95 100 105 110 115 12020
15
10
5
0
5
10
15
20
Payoff
Spotatexpiry, ST
80 85 90 95 100 105 110 115 12020
15
10
5
0
5
10
15
20
Payoff
Spotatexpiry, ST
80 85 90 95 100 105 110 115 12020
15
10
5
0
5
10
15
20
Payoff
Spotatexpiry, ST
4 5 6
80 85 90 95 100 105 110 115 12020
15
10
5
0
5
10
15
20
Payoff
Spotatexpiry, ST
80 85 90 95 100 105 110 115 12020
15
10
5
0
5
10
15
20
Payoff
Spotatexpiry, ST
80 85 90 95 100 105 110 115 12020
15
10
5
0
5
10
15
20
Payoff
Spotatexpiry, ST
The dash and dotted lines are payoffs for the two composition instruments.
The solid lines are payoffs of the target.Liuren Wu (Baruch) Options Trading Strategies Options Markets 4 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
5/18
The linkage between put, call, and forward
The above conversions reveal the following parity condition in payoffs of put,call, and forward at the same strike and maturity:
Payoff from a call Payoff from a forward = Payoff from a put
Payoff from a put + Payoff from a forward = Payoff from a call
Payoff from a call
Payoff from a put = Payoff from a forwardIf the payoff is the same, the present value should be the same, too (put-callparity):
ct pt = er(Tt)(Ft,T K).
At a fixed strike (K) and maturity T, we only need to know the two pricesof the following three: (ct, pt, Ft,T).One of the three contracts is redundant.
Liuren Wu (Baruch) Options Trading Strategies Options Markets 5 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
6/18
Review: Create forward using spot and bond
In the absence of forward, use spot and bond:
Can you use a spot and bond to replicate a forward payoff?
Whats the payoff function of a zero bond?
Liuren Wu (Baruch) Options Trading Strategies Options Markets 6 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
7/18
Popular payoff I: Bull spread
80 85 90 95 100 105 110 115 12020
15
10
5
0
5
10
15
20
Payoff
Spotatexpiry, ST
Can you generate the above payoff structure (solid blue line)using (in addition to cash/bond):
two calls
two putsa call, a put, and a stock/forward
Who wants this type of payoff structure?
Liuren Wu (Baruch) Options Trading Strategies Options Markets 7 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
8/18
Generating a bull spread
Two calls: Long call at K1 = $90, short call at K2 = $110, short a bond
with $10 par.Two puts: Long a put at K1 = $90, short put at K2 = $110, long a bondwith $10 par.
A call, a put, and a stock/forward: Long a put at K1 = $90, short a call at
K2 = $110, long a forward at K = 100 (or long a stock, short a bond at$100 par).
80 85 90 95 100 105 110 115 12020
15
10
5
0
5
10
15
20
25
30
Payoff
Spotatexpiry, ST
80 85 90 95 100 105 110 115 12030
25
20
15
10
5
0
5
10
15
20
Payoff
Spotatexpiry, ST
80 85 90 95 100 105 110 115 12025
20
15
10
5
0
5
10
15
20
Payoff
Spotatexpiry, ST
Liuren Wu (Baruch) Options Trading Strategies Options Markets 8 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
9/18
Pointers in replicating payoffs
Each kinky point corresponds to a strike price of an option contract.
Given put-call party, you can use either a call or a put at each strike point.
Use bonds for parallel shifts.
A general procedure using calls, forwards, and bonds
Starting from the left side of the payoff graph at ST = 0 and progressto each kinky point sequentially to the right.
If the payoff at ST = 0 is x dollars, long a zero-coupon bond with anx-dollar par value. [Short if x is negative].
If the slope of the payoff at ST = 0 is s0, long s0 shares of acall/forward with a zero strike A call at zero strike is the same as aforward at zero strike. [Short if s0 is negative.]
Go to the next kinky point K1. If the next slope (to the right of K1 iss1, long (s1 S0) shares of call at strike K1. Short when the slopechange is negative.
Go to the next kinky point K2 with a new slope s2, and long (s2 s1)shares of calls at strike K2. Short when the slope change is negative.
Keep going until there are no more slope changes.
Liuren Wu (Baruch) Options Trading Strategies Options Markets 9 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
10/18
Pointers in replicating payoffs, continued
A general procedure using puts, forwards, and bonds
Starting from the right side of the payoff graph at the highest strikeunder which there is a slope change. Let this strike be K1.
If the payoff at K1 is x dollars, long a zero-coupon bond with anx-dollar par value. [Short if x is negative].
If the slope to the right of K1 is positive at s0, long s0 of a forward atK1. Short the forward if s0 is negative.
If the slope to the left of K1 is s1, short (s1 s0) shares of a put at K1.Long if (s1 s0) is negative.
Go to the next kinky point K2. If the slope to the left of K2 is s2, short(s2 s1) put with strike K2.
Keep going until there are no more slope changes.
Liuren Wu (Baruch) Options Trading Strategies Options Markets 10 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
11/18
Example: Bear spread
80 85 90 95 100 105 110 115 12020
15
10
5
0
5
10
15
20
Payoff
Spotatexpiry, ST
How many (at minimum) options do you need to replicate the bear spread?
Do the exercise, get familiar with the replication.
Who wants a bear spread?
Liuren Wu (Baruch) Options Trading Strategies Options Markets 11 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
12/18
Example: Straddle
80 85 90 95 100 105 110 115 12010
5
0
5
10
15
20
25
30
Payoff
Spotatexpiry, ST
How many (at minimum) options do you need to replicate the straddle?
Do the exercise, get familiar with the replication.
Who wants long/short a straddle?
Liuren Wu (Baruch) Options Trading Strategies Options Markets 12 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
13/18
Example: Strangle
80 85 90 95 100 105 110 115 12010
15
20
25
30
35
40
Payoff
Spot atexpiry, ST
How many (at minimum) options do you need to replicate the strangle?
Do the exercise, get familiar with the replication.
Who wants long/short a strangle?
Liuren Wu (Baruch) Options Trading Strategies Options Markets 13 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
14/18
Example: Butterfly spread
80 85 90 95 100 105 110 115 12020
15
10
5
0
5
10
15
20
25
30
Payoff
Spotatexpiry, ST
How many (at minimum) options do you need to replicate the butterflyspread?
Do the exercise, get familiar with the replication.
Who wants long/short a butterfly spread?
Liuren Wu (Baruch) Options Trading Strategies Options Markets 14 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
15/18
Example: Risk Reversal
80 85 90 95 100 105 110 115 12010
8
6
4
2
0
2
4
6
8
10
Payoff
Spotatexpiry, ST
80 85 90 95 100 105 110 115 12010
8
6
4
2
0
2
4
6
8
10
Payoff
Spotatexpiry, ST
How many (at minimum) options do you need to replicate the risk reversal?
Do the exercise, get familiar with the replication.
Who wants long/short a risk reversal?
Liuren Wu (Baruch) Options Trading Strategies Options Markets 15 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
16/18
Smooth out the kinks: Can you replicate this?
80 85 90 95 100 105 110 115 1200
50
100
150
200
250
300
350
400
Payoff
Spot atexpiry,ST
How many options do you need to replicate this quadratic payoff?
You need a continuum of options to replicate this payoff. The weight on each strike K is 2dK.
Who wants long/short this payoff? The variance of the stock price is E[(ST Ft,T)
2]. Variance swap contracts on major stock indexes are actively traded.
Liuren Wu (Baruch) Options Trading Strategies Options Markets 16 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
17/18
Replicate any terminal payoff with options and forwards
f(ST) = f(Ft) bonds+f(Ft)(ST Ft) forwards
+
Ft
0f(K)(K ST)
+dK
Ftf(K)(ST K)
+dK
OTM options
What does this formula tell you? With bonds, forwards, and European options, we can replicate any
terminal payoff structures. More exotic options deal with path dependence, correlations, etc.
You do not need to memorize the formula.
Proof: Optimal positioning in derivative securitiesby Carr and Madan,Quantitative Finance, 2001.
Liuren Wu (Baruch) Options Trading Strategies Options Markets 17 / 18
http://find/http://goback/8/3/2019 Derivative Option Strategies_Lecture
18/18
Replication applications
Replicate the return variance swap using options and futures.
Variance risk premia, RFS, forthcoming.
Based on the replication idea, think of ways to summarizing the informationin the options market.
Information about the directional movement of the underlying. Information about return variance. Information about large movements of a certain direction. Information about large movements of either direction.
Example: Price discovery in the U.S. stock and stock options markets: Aportfolio approach, Review of Derivatives Research, 2006, 9, 3765.
Caveat: Far out-of-the-money options may not be actively traded. Quotesmay not be reliable.Example: ATM volatility versus synthetic variance swap.
Liuren Wu (Baruch) Options Trading Strategies Options Markets 18 / 18
http://find/http://goback/