# Can anyone help me with this Put/Call option question please!!?

Options Exercises II

The current price of Widget Inc (WI) is \$10 per share. Joe expects the price if WI to fall to at least \$7 over the next 60 days. Jane on the other hand thinks that the price of WI will rise over the next 60 days and top out at \$11. Assuming no transaction costs:

a) Would Joe be interested in buying a WI put option with a strike price of \$8 that sells for \$0.5 dollars (50 cents), to expire 60 days from now? Explain why/ why not.

b) Would Jane be interested in writing (selling) a put option with a strike price of \$8 for fifty cents? Explain why/why not.

c) At this point in time, what is the maximum price Joe would be willing to pay for this put option?

d) At this point in time what is the minimum Jane would be willing to accept for this put option?

e) Does there appear to be a market for the WI, \$8 (60 day) put option? What factors would determine the actual price of the \$8 put option?

f) Calculate the gain/loss for Joe and Jane if the WI reaches a price \$7.25 and Joe exercises his option on 100 shares.

Relevance

<<<) Would Joe be interested in buying a WI put option with a strike price of \$8 that sells for \$0.5 dollars (50 cents), to expire 60 days from now? Explain why/ why not.>>>

The answer they want is probably "yes" since Joe will at least double his money if the price of WI goes down to \$7.00 per share.

In reality most option traders realize their predictions are not that good so they will want a better than 1:2 risk:reward ratio for an unhedged long position.

<<<b) Would Jane be interested in writing (selling) a put option with a strike price of \$8 for fifty cents? Explain why/why not.>>>

The answer they probably want is "yes" since she thinks the stock will go up and will keep the option premium as a profit as long as the stock does not go down more than 20%.

In reality Jane is more likely to base her decision upon the amount of risk she believes is present in WI stock.

<<<c) At this point in time, what is the maximum price Joe would be willing to pay for this put option?>>>

The answer they probably want is \$1.00 less the amount of interest Joe could get for \$1.00 in 60 days. So, for example, if Joe could get 12% interest that would be \$0.02 in interest so the most he should be willing to pay would be \$1.00 - \$0.02 = \$0.98.

In reality, assuming Joe understands options, the most he should be willing to pay would be based upon the the options pricing model and his expectation for volatility in the stock over the next 60 days.

<<<d) At this point in time what is the minimum Jane would be willing to accept for this put option?>>>

I have no idea how they want you to calculate this from the information given.

In reality, assuming Jane understands options, the least she should be willing to accept would be based upon the the options pricing model and her expectation for volatility in the stock over the next 60 days.

<<<e) Does there appear to be a market for the WI, \$8 (60 day) put option?>>>

That cannot be determined from the information given.

<<<What factors would determine the actual price of the \$8 put option?>>>

The stock price (\$10)

The strike price (\$8)

The time until expiration (60 days)

Any dividends with ex-dates prior to expiration

The type of settlement (American or European)

The "risk-free" interest rate

The implied volatility

<<<f) Calculate the gain/loss for Joe and Jane if the WI reaches a price \$7.25 and Joe exercises his option on 100 shares.>>>

Since the effective trade price would be \$8.00 - \$0.50 = \$7.50 Joe would show a profit, and Jane would show a loss, of (\$7.50 - \$7.25) x 100 = \$25.00

Source(s): A basic knowledge of options.
• Login to reply the answers
• Anonymous
4 years ago

<<<Q. Assume put-call parity holds. Now show that put delta is equal to call delta minus 1.>>> If you ignore interest rates, put call parity simply says P + S = C + E where: P = the market price of the put S = the market price of the stock C = the market price of the call E = the exercise price of both the call and the put Rearranging this a little, you get P - C = E - S The exercise price is a constant, so if the stock price changes it is clear that P - C must also change by the same amount. By definition, delta is the amount that a value of security changes as a fraction of change in the price of an underlying security. That means we know delta (P) - delta (C) = -delta (S) For a security underlying an option, the delta must be 1.00, so delta (P) - delta (C) = -1.00 or delta (P) = delta (C) - 1.00 A more accurate version of put call parity states that P + S = C + E * [1/(1+i)] ^n where: P = the market price of the put S = the market price of the stock C = the market price of the call E = the exercise price of both the call and the put i = the risk free rate n = the number of years until the expiration date of the options The previous proof still works since "E * [1/(1+i)] ^n" is still a constant that does not depend of the price of the stock.

• Login to reply the answers