Question

The table below gives price information on options for use in problems. Also assume that the spot price is currently $86 and the interest rate is a constant 3.5% (continuously compounded and identical for January and February to simplify calculations). Finally, assume that there is exactly one month until the January expiration and exactly two months until the February expiration.

	CALLS		PUTS
STRIKE	JANUARY	FEBRUARY	JANUARY	FEBRUARY
80	6.8	7.05	0.57	0.59
85	2.24	2.56	1	1.07
90	0.24	0.31	3.98	4.02

What are the intrinsic and time values of the January 80 strike call option?

Show that put-call parity holds for the February 80 strike options.

Calculate the present value of the arbitrage profit that can be earned from the February 90 strike options.

NO EXCEL PLEASE SHOW YOUR WORK IN DETAIL

Answer 1

1. Intrinsic value = Spot price - Strike price =86 - 80 = 6

Time value = Call option value - intrinsic value = 6.8 - 6 = 0.8

As per Put Call Parity:

C - P = S - K* e^(-r*t)

^where

C is the current call option price

P is the put option price

S is the spot price

K is the strike price

r is the risk free interest rate

t is the time to expiry

In this case,

LHS = C - P =7.05 - 0.59 = 6.46

RHS = 86 - 80 * e(-0.035 * 2/12) = 6.46

LHS = RHS. Hence, PCP holds true

Arbitrage profit

Let us calculate the fair value of the put option given other variables:

P* = C - S + K*e^(-r*t) = 0.31 - 86 + 90*e(-0.035*2/12) = 3.786528

P =4.02

Present value of gain = (4.02 - 3.786528) * e(-0.035*2/12) = 0.232114