Question

1. Assume that a stock price is $120 per share and the stock does not pay any dividend. The options are six-month European options and the exercise price of these options is $120 per share. The call price is $10 per share and the put price is $8 per share.
   1. Use the put option, the call option, and the underlying stock to create a portfolio which will let you borrow $120,000 (face amount) for 6 months through the option markets.
   2. What is the rate of interest on the money that you borrow in a)? Give this rate per annum with continuous compounding.

Answer 1

a]

Borrowing is done by shorting a risk-free bond.

A synthetic short position on $120,000 face value risk-free bond is created as below :

• Buy 1000 call options
• Sell 1000 put options
• Short 1000 shares of the underlying stock

b]

Put call parity equation is given as :

C + (X / e^rt) = S + P, where

C = price of call option

X = exercise price

S = price of underlying stock

P = price of put option

r = risk free rate

t = time to expiry (in years)

Substituting the values into this equation, we get :

10 + (120 / e^r*0.5) = 120 + 8

120 / e^r*0.5 = 118

e^0.5r = 120 /118

0.5r = LN(120/118)

r = 3.36%

The rate of interest is 3.36%