Question

In: Finance

Assume that the combined value of the put and stock exceed the value of the actual...

Assume that the combined value of the put and stock exceed the value of the actual call buy more than the present value of exercise price, that is ? + ?0 > ? + ?? −??? . Show how an arbitrate profit can be made.

Expert Solution

Put Call Parity Theorm:

It shows the long term equilibrium relation between Value of call with certain exercise price, Value of put with same exercise price, excercise price, exercise date and stock price today.

Vc + PV of Strike Price = Vp + Stock price

Vc = Value of call
Vp = Value of Put

If the equation doesn't hold good, there will be arbitrage profit.

In the given case, Vp & Stock Price is higher than Vc & PV of Strike Price.

Then with the below steps, we can get arbitrage profit.

If (VC + PV of Strike Price) < ( Vp + Stock Price ) :

Startegy -

Hold a Call Option
Short sell a share
Write a Put Option

Initial Cash Inflow:
= Premium on Put Option + Stock Price - Premium on Call option

Invest Amount in bank:

Invest the net proceeds from above step.

Maturity Value of amount invested :
= Amount invested * e ^ rt
r - Int rate per anum
t - Time in Years

On Maturity:

Amount required to buy the stock and clear the short position -

Alt - 1:
If the Stock price on Maturity Date is More Than Strike Price, Put potion will be lapsed. Being Holder of call option, stock will be purchased at strike Price.

Alt - 2:
If the Stock price on Maturity Date is less than Strike Price, Call potion will be lapsed. Holder of put option, We will exercise his right and We need to buy the stock at strike price.

i.e in any case, we would be able to purchase at strike price.

Arbitrage gain on Maturity date = Mayurity Value of Investemnt - Strike Price

Arbitrage gain in Today's Value:
= Arbitrage gain on maturity * e ^-rt

Pls comment, if any further assistance is required.

jeff jeffy answered 2 years ago

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