Need help with Question 4

We covered this in lectures. This is a contract that matures at time T2 but at the time the contract is enteredinto we don't know if it is a call or a put option. This is contract allows us to make a decision at time T1 about whether we want to have a European call option or a European put option over some asset S that matures at time T2. There are 2 types of chooser option: the "simple chooser" and the "complex chooser".

Your task for this question is to write a spreadsheet to do a valuation of these chooser options. Your spreadsheet will be marked on the basis of whether it works or not. It should be able to handle a general setof inputs, not just the inputs set out below. You should design this spreadsheet so it makes use of the spreadsheet for computing the bivariate normal cumulative distribution function M(a,b,p). You can copy this M function spreadsheet and make it one of the sheets in the workbook for this assignment.

The simple chooser:

The value of the simple chooser option at time T1 isV(T)=max(C(S,X,r,y,,),P(S,X,r,y,,))

1

this is the higher of the value of a standard European call and a standard European put option over the

underlying asset (S) , with a term to maturity of =T T21

Note that both the call and the put have the same remaining term to maturity and the same exercise price X. The value at time 0 of this contract is

yT21rT22 rT22yT21value=Se N(d)Xe N(d) Xe N+(d')SeN(d')where

d=1lnS+ry+12Td=dT12212

T

T

11

T2X2

d'=1lnS+ry+12Td'=d'T

11211TX2

1

d'=1lnS+ry+12(TT)

321TTK2

1

T1 2111

21

The Complex Chooser:

This is more difficult to value and we have to use the M(a,b,p) function to value it.

The value of the complex chooser option at time T1 (which is when we are allowed to choose between a call and a put) is

V(T)=max(C(S,X,r,y,,T T),P(S,X,r,y,,T T))

T2 31

this is the higher of the value of a standard European call and a standard European put option over the

underlying asset (S)

Note that here the call and the put have two different maturity dates (T2 for the call and T3 for the put) and they also have different exercise prices (X1 for the call and X2 for the put)

6

the valuation formula for this complex chooser has 4 parts:

' 1TS2

(0)

=2(,1,1)12(1,12,1)3(,2,2) +23(+1,2+3,2)

Where

x=1lnS+ry+12T

1

y=1lnS+ry+12T

12T2X12

y=1lnS+ry+12T23

T3X22=(TT)=(TT)

112213

y=dividend yield; r=risk free rate

S' is the critical value of S that makes the value of the call option equal to the value of the put option attime T1 when we have to choose which of the 2 options we want to have.

S'isthesolutionoftheequationC(S',X,r,y,,TT)=P(S',X,r,y,,TT)121231

Note that you will have to solve the problem of computing S' as part of this assignment. Your spreadsheet should be able to deal with the general case, not just the specific parameter inputs set out below.

Assume the following values for the various variables above, calculate the value of a complex chooser andthe value of a simple chooser option.

S=50,r2.00=%,y10%, =44%=X1=24= strike price of call option

X2=30= strike price of put option

T=1.5 = date when we choose between call and put1

T2=2.0=maturitydateforcalloptionT3=2.5=maturitydateforputoption

For the simple chooser assume the put has the same expiry date and exercise price as the call above.

7

YOUR TASK

1) SEE THE ATTACHED INSTRUCTIONS FOR BUILDING A SPREADSHEET FOR A BINOMIAL BLACK SCHOLES HYBRID VALUATION OF COMPOUND OPTIONS

ADAPT / MODIFY THIS SPREADSHEETS SO YOU CAN DO A BINOMIAL BLACK SCHOLES HYBRID VALUATION OF BOTH A SIMPLE AND A COMPLEX CHOOSER OPTION

25 MARKS

2) SEE THE ATTACHED INSTRUCTIONS FOR BUILDING A SPREADSHEET FOR IMPLEMENTING THE ANALYTIC VALUATION OF COMPOUND OPTIONS

ADAPT / MODIFY THIS SPREADSHEET SO YOU CAN DO AN ANALYTIC VALUATON OF BOTH THE COMPLEX CHOOSER OPTION

25 MARKS