Question

A stock sells for $60 and the risk free rate of interest is 5 percent. | ||||||

A call and a put on this stock expire in one year and both options have an exercise price of $55. | ||||||

How would you trade to create a synthetic call option? | ||||||

If the put sells for $3, how much is the call option worth ? Assume continuous compounding? |

Answer #1

As per put-call parity,

Cash investment + Call = Stock + Put

Therefore to create synthetic call option, I would buy borrow funds and buy stock and buy put option

Amount to be borrowed = PV of strike price

As per put call parity,

Cash investment + call premium = stock price + put premium

{Note that strike of call and put option should be same and cash investment should be present value of strike of call or put}

Cash investment + call premium = stock price + put premium

55 / e^{5%} + call premium = 60 + 3

Call price = 63 - 57.82 = **$ 5.18**

Thumbs up please if satisfied. Thanks :)

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