Question

In: Finance

1. Consider an at-the-money European put option with a strike price of $30 and 6 months...

1. Consider an at-the-money European put option with a strike price of $30 and 6 months until

expiration.The underlying stock does not pay dividends and has a historical volatility of 35%. The risk-free rate is 3%.

a. (5 points) What is the options delta?

b. (5 points) What is the value of the option?

c. (5 points) If the stock price immediately changed to $24, what would be the estimated price of the option, using the delta approximation?

d .(5 points) Now consider the call option with the same information; compute its delta.

e. (5 points) If you purchase 10 of the put option and 5 of the call option, what is the delta of the resulting portfolio?

Solutions

Expert Solution

a,b and d) are answered above

c) If stock price changed to 24, put price will rise by 6*0.4269=2.5614 and it will become 2.7145+2.5614=5.2759

e) Delta of portfolio=10*(-0.4269)+5*0.5731=-1.4035

jeff jeffy answered 2 years ago
Next > < Previous

Related Solutions

Consider a European put option on a share of a company. The strike price is 50....
Consider a European put option on a share of a company. The strike price is 50. The investors pays an option premium of 10. If the payoff for the investor (not taking into account the option premium) is 10, then what is the profit of the option writer (taking everything into account)? Please leave answer to 4 decimal places
Consider a European put option on a share of a company. The strike price is 50....
Consider a European put option on a share of a company. The strike price is 50. The investors pays an option premium of 10. If the payoff for the investor (not taking into account the option premium) is 10, then what is the profit of the option writer (taking everything into account)?
1.The price of a three-month European put option on a stock with a strike price of...
1.The price of a three-month European put option on a stock with a strike price of $60 is $5. There is a $1.0067 dividend expected in one month. The current stock price is $58 and the continuously compounded risk-free rate (all maturities) is 8%. What is the price of a three-month European call option on the same stock with a strike price of $60? Select one: a. $5.19 b. $1.81 c. $2.79 d. $3.19 2.For the above question, if the...
-European call and put options with 3 months of expiration exist with strike price $30 on...
-European call and put options with 3 months of expiration exist with strike price $30 on the same underlying stock. The call is priced at $3.5, the put is priced at $1.25, while the underlying is currently selling for $28.5. a) What is the net profit for the buyer of the call if the stock price at expiration is $36? b) What is the net profit for the seller of the call if the stock price at expiration is $38?...
Consider a European call option and a put option on a stock each with a strike...
Consider a European call option and a put option on a stock each with a strike price of K = $22 and each expires in six months. The price of call is C = $3 and the price of put is P = $4. The risk free interest rate is 10% per annum and current stock price is S0 = $20. Show how to create an arbitrage strategy and calculate the arbitrage traders profit.
The price of a European put that expires in six months and has a strike price...
The price of a European put that expires in six months and has a strike price of $100 is $3.59. The underlying stock price is $102, and a dividend of $1.50 is expected in four months. The term structure is flat, with all risk-free interest rates being 8% (cont. comp.). What is the price of a European call option on the same stock that expires in six months and has a strike price of $100? [1 marks] Explain in detail...
A European call option and put option on a stock both have a strike price of...
A European call option and put option on a stock both have a strike price of $21 and an expiration date in 4 months. The call sells for $2 and the put sells for $1.5. The risk-free rate is 10% per annum for all maturities, and the current stock price is $20. The next dividend is expected in 6 months with the value of $1 per share. (a) describe the meaning of “put-call parity”. [2 marks] (b) Check whether the...
A European call option and put option on a stock both have a strike price of...
A European call option and put option on a stock both have a strike price of $21 and an expiration date in 4 months. The call sells for $2 and the put sells for $1.5. The risk-free rate is 10% per annum for all maturities, and the current stock price is $20. The next dividend is expected in 6 months with the value of $1 per share. (a) In your own words, describe the meaning of “put-call parity”. (b) Check...
A European call option and put option on a stock both have a strike price of...
A European call option and put option on a stock both have a strike price of $25 and an expiration date in four months. Both sell for $4. The risk-free interest rate is 6% per annum, the current stock price is $23, and a $1 dividend is expected in one month. Identify the arbitrage opportunity open to a trader.
Consider a 1000-strike put option on the S&R index with 6 months to expiration. At the...
Consider a 1000-strike put option on the S&R index with 6 months to expiration. At the time the option is written, the put writer receives the premium of $74.20. Suppose the index in 6 months is $1100. The put buyer will not exercise the put. Thus, the put writer keeps the premium, plus 6 months’ interest, for a payoff of 0 and profit of $75.68. If the index is $900 in 6 months, the put owner will exercise, selling the...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT