You have written (sold) a three-month European call option at a strike price of $500. The current stock price (So) is $492.00, the annual risk-free interest rate is 4%, and the volatility of the underlying is 10%. Construct a delta hedge of this position using the underlying asset. Report your answer in the number of shares of the underlying purchased/sold. (Positive values indicate a purchase, negative a short)

You have written (sold) a three-month European call option at a strike price of $500. The current stock price (So) is $492.00, the annual risk-free interest rate is 4%, and the volatility of the underlying is 10%. Construct a delta hedge of this position using the underlying asset. Report your answer in the number of shares of the underlying purchased/sold. (Positive values indicate a purchase, negative a short)

FINANCIAL ACCOUNTING

10th Edition

ISBN:9781259964947

Author:Libby

Publisher:Libby

Chapter1: Financial Statements And Business Decisions

Section: Chapter Questions

Problem 1Q

See similar textbooks

Similar questions

The Black-Scholes model is used to value call options on the stock of National Co. The following information was identified:·       The share price is P43.·       The option matures in 6 months·       The risk-free rate is 2%.·       Price of the option is at P43.What is the exponent of “e” for in computing the value of the call option using the Black-Scholes model?
You are given the following information about the stock of Company ABC: Share price $80 risk free rate of interest is 6%, time to expiration is 6 months, annualised standard deviationis 0.5 and exercise price is $85. Calculate the appropriate call value of the stock according to the Black-Scholes option pricing formula.                                                                                               (Show your workings in full)                                                                                                                         Calculate an appropriate put premium.                (Show your workings in full)
The Black-Scholes model is used by Bulldogs Inc. to value call options on the stock of National Inc. The following information was determined by the analyst:·       The share price is P30.·       The price of the option is at P32.·       The risk-free rate is 3%.·       The option matures in 6 monthsIn the formula of the current value of the call option under the Black-Scholes model, what is the exponent of “e” be?
You observe the price of a European put option that expires in nine months and has a strike price of$45 is $3. The underlying stock price is $49.50. The term structure is flat, with all risk-free interestrates being 8%.a. What is the price of a European call option that expires in nine months and has a strike priceof $45? b. You observe next that the price of the call option (in part (a)) in the market is $9.59. Statewhy an arbitrage opportunity exists and explain how you would take advantage of thisopportunity. (Hint: answer should include an outline general strategy, net cost ofstrategy at initiation and net profit at expiration using the numbers in the question)
A collar is established by buying a share of stock for $46, buying a 6-month put option with exercise price $43, and writing a 6-month call option with exercise price $49. On the basis of the volatility of the stock, you calculate that for a strike price of $43 and expiration of 6 months, N(d₁) = .6974, whereas for the exercise price of $49, N(d₁) = 0.6504. What will be the gain or loss on the collar if the stock price increases by $1? (Round your answer to 2 decimal places. Omit the "$" sign in your response.) Collar gain by b-1. What happens to the delta of the portfolio if the stock price becomes very large? (Omit the "$" sign in your response.) a. Delta of the portfolio approaches .05 b-2. What happens to the delta of the portfolio if the stock price becomes very small? (Omit the "$" sign in your response.) Delta of the portfolio approaches
You buy a share of stock, write a 1-year call option with X = $55, and buy a 1-year put option with X = $55. Your net outlay to establish the entire portfolio is $54. The stock pays no dividends. a. What is the payoff of your portfolio? Payoff b. What must be the risk-free interest rate? (Round your answer to 2 decimal places.) Risk-free rate %
The price of a European call option on a non dividend paying stock with a strike price of $79 is $8. The stock price is $75, the continuously compounded risk-free rate (all maturities) is 4.50% and the time to maturity is one year. a. What is the price of a one year European put option on the stock with a strike price of $79? (Hint: Use the Put-Call Parity Formula).
Suppose a one-year European put option on a stock has an exercise price of $30 and oneyear European call option on the same stock has the same exercise price of $30. The call is worth 3$ and the put is worth 2$. If the one-year interest rate is 1.5%, what is the price of the underlying stock, assuming no arbitrage opportunity?
Optival’s stock is currently trading at $60 per share with a historical volatility of 20%. The risk-free rate is 4%. Consider a European call and put option on Optival’s stock with an exercise price of $55 that expires in 2 years. Use excel or a similar program to determine the option price using the Black-Scholes formula. (a): What is the value the European call and put option on Optival’s stock with a strike price of $60? (b): To the nearest cent, how much does the option value change for the following adjustments to the input values: ∆ in Call Value ∆ in Put Value ↑ stock price by $1 to $61 ↑ strike price by $1 to $56 ↑ the rF by 1% to 5% ↑ volatility by 1% to 21% ↑ time to maturity by 1 yr (c): Why does the value of the call increase by less than $1 when the stock price increases by $1? (d): To the nearest percent and holding all else constant, how high would the risk-free rate need to be for a 1 year increase in time to maturity to have a negative impact on the value of…
Determine the risk-neutral value for a European put option (for a FLB (First Local Bank) share) that expires in eight months. The strike price is R500 and the current price is R650. The interest rate is 11%, and the volatility of the security is 0.026. *DO NOT USE EXCEL OR ANY OTHER PLATFORM, SHOW STEP-BY-STEP CALCULATION
In a financial market a stock is traded with a current price of 50. Next period the priceof the stock can either go up with 30 per cent or go down with 25 per cent. Risk-freedebt is available with an interest rate of 8 per cent. Also traded are European optionson the stock with an exercise price of 45 and a time to maturity of 1, i.e. they maturenext period.i) Find prices of Arrow-Debreu securities.
Please show step by step work (not in excel): What is the call option premium given the following information? What would happen to the call price if the company initiated and paid a dividend before the expiration of the option? What would happen to the call premium if the expiration of the option expanded beyond the current 9 months? Stock price $36.00 Strike price $30.00 Volatility 16% Dividend Yield 0.00 Time 0.75 Riskfree Rate 2.70%