Question

1. 1-year put option on the same stock with an exercise price of $35 costs $2.1, the stock price is $33 and the interest rate on a bank deposit per annum is 10%.
   a) Use the put-call parity relation to calculate the price of a 1-year European call option on the same stock.

   b) If the market price of the call option is $4, is there an arbitrage opportunity? c) If so, define arbitrage strategy.

Answer 1

Part A>

We have we have the following information for a call and a put option on stock.

Exercise price: $35

Call option price: ?

Put option price: $2.1

Risk-free rate: 10%

Current market price of XYZ: $33

Time to maturity: 1 years

Let’s plug these values in the put-call parity equation:

C + K/(1+r)^T = P + S

C + 35/(1.1)^1 = 2.1 + 33

C = 3.28

Hence, the value of the European Call option is $3.28

Part B>

Now the value of C is also given as C = $4.

Putting again in the Put-Call parity equation

C + K/(1+r)^T = P + S

4 + 35/(1.1)^1 = 2.1 + 33

35.82 = 35.1

As we can see, the left hand side is greater than the right hand side by (35.82 - 35.1) = 0.72

To make use of this arbitrage opportunity, we will buy the Put and sell the call.

1. Buying put: We buy a put option and pay the $2.1 premium. We also buy the stock and pay $33. The total cash outflow is $35.1

2. Selling call: We receive a total of $35.82 for the call option. That is we receive $4 as premium for the call option and get $31.82 from the bond at 10%.

3. Net cash inflow: Our net cash inflow is (35.82 - 35.1) = $0.72

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