Question

~~~In Excel~~~

**Question 2.** 1-month call and put price for
European options at strike 108 are 0.29 and 1.70, respectively.
Prevailing short-term interest rate is 2% per year.

a. Find current price of the stock using the put-call parity.

b. Suppose another set of call and put options on the same stock at strike price of 106.5 is selling for 0.71 and 0.23, respectively. Is there any arbitrage opportunity at 106.5 strike price? Answer this by finding the amount of arbitrage profit available at strike price of 106.5. (Hint: Use the price found in part (a) to find the value of both sides of the put-call parity. If the two sides are not equal, then there is some arbitrage opportunity.)

c. What would be the strategy to take advantage of arbitrage opportunity at 106.5, if there is any? (Hint: State whether you would have to be long/short in all the 4 instruments (put, call, stock, bond) that are used in the put-call parity)

~~~In Excel~~~

Answer #1

Hello

(a)

Strike Price | 108 | ||

Call Price | 0.29 | ||

Put Price | 1.7 | ||

Interest Rate | 2% p.a. | ||

Put call Parity : | |||

C + PV(X) = P + S | |||

Call Price | 0.29 | ||

+ | PV(X) | [108/(1.02)^(1/12)] | 107.82 |

- | Put Price | 1.70 | |

= | Spot Price |
106.41 |

(b) Options of Strike Price 106.5

Call Price + PV(X) = 0.71 + 106.32 = 107.03

Put Price + Spot Rate = 0.23 + 106.41 = 106.64

Since, both sides are not equal, there lies an arbitrage
opportunity, profit available **= $107.03 - $106.64 =
$0.39**

(c) The appropriate strategy is to go long on the put option and the stock and to go short on call option and a fixed income instrument with interest rate 2% er year.

I hope this clears your doubt.

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