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A stock price is $74, and current risk free interest rates are 2%. If the put...

A stock price is $74, and current risk free interest rates are 2%. If the put option with a $100 strike price expires in 6 months, and the call option is trading at $26.25, how would you arb this option?

Solutions

Expert Solution

Stock current price = $74

Put option Strike price = $100

Expiry = 6 months

Risk-free rate = 2%

Risk free rate for 6 months = 2%*6/12 = 1% or 0.01

Call option price = $26.25

Present value of E.P. = E.P./(1+i)

= 100/(1+0.01)

= 99.009900990099

Theoritical Call option price = Current market price - P.V. of Exercise price

= 74 - 99.0099

= -25.01

Call option theoritical price is -$25.01. while actual price is $26.25. So Call option is overpricing. it should be sold.

Arbitrage strategy

Sell one call and Buy stock

At current time, Premium will be received from selling call $26.25

Buy stock @ 74 -74

Total outflow -$47.75

At 6 months, if price of stock is 120

VC for buyer = stock price - E.P.

120 - 100 = 20

Outflow for writer -$20

Selling stock at $120 +120

Interest cost on initial investment

(47.75 * 1%) -0.4775

Total inflows 99.5225

Total gain = total inflows - total outflows

= 99.5225 - 47.75 = 51.7725

Present value of gain = 51.7725/1.01 = $51.26

So, Arbitrage profit of $51.26 will be earned.

jeff jeffy answered 1 year ago

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