Question

Calculate the cost of your instrument for the following: you wish to create a financial instrument that has a payoff in 6 months’ time equal to the maximum value of $2,000 and $2,000 + $0.5*(S&P Index in 6 months’ time – 3,200). The 6-month call and put options with strike price 3,200 is trading at 120 and 110, respectively.

Answer 1

Solution:

Put-call parity equation

C + Present Value (X) = S+P

it can be written as

C+X/(1+r)^t = S+P

Where,

C= call premium

P = put premium

X= strike price

r= interest

t= time period

S= initial price

Therefore,

C+ X/(1+r)^t = S+P

3200/(1+r)^t = 3200 +110 - 120

(1+r)^t = 3200 / (3200+110-120)

(1+r)^t = 3200 / 3190

(1+r)^t = 1.0031348

Now,

Payoff = Max [2000,spot price at expiration - strike price]

= Max [2000,2000+0.5 * (St - 3200) ]

= 2000 + Max (0, 0.5 * St - 3200)

= 2000 + 0.5 * Max(0,St - 3200)

The above payoff seems like derived from 2000 + 0.5 *C

Where,

C indicates call option with strike price of 3200

Hence,

Cost = 2000 / (1+r)^t + (0.5 *120)

Substitute the value of (1+r)^t = 1.0031348 in above equation

we get,

= 2000 / 1.0031348 + 60

= 1993.74999 + 60

= 2053.75

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