a.
To compute: The payoff of the portfolio in the given conditions.
Introduction:
Net Payoff: Normally, the payoff in financial terminology refers to the amount received as
b.
To compute: The risk-free interest rate of the portfolio, the condition in which stock pays no dividends.
Introduction:
Risk-free interest rate: When an investment is made in securities that do not have any risk of any financial losses in a termed period, the rate at which the return is earned is termed as a risk-free interest rate.
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INVESTMENTS-CONNECT PLUS ACCESS
- You buy a share of stock, write a 1-year call option with X = $85, and buy a 1-year put option with X = $85. Your net outlay to establish the entire portfolio is $83.3. Required: What is the payoff of your portfolio? What must be the risk-free interest rate? The stock pays no dividends. Note: Round your answer to 2 decimal places.arrow_forwardD3) Finance What is the probability that the put option is OTM at maturity if: the Stock is S = $195.00, no dividend is paid, the risk-free rate is r = 2.40%, the strike price is K = 209.00, the maturity is T = 23 months and the parameters are d1 = 0.2328 and d2 = -0.3175?arrow_forwardConsider a put option on a stock that curretly sclls for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (a) Calculate the value of the put option using the risk-neutral valuation relationship (RNVR). Explain the reasoning behind your calculations. (b) Calculate the value of the put option by using first principles (No Arbitrage prin- ciples). Explain the reasoning behind your calculations. (c) What is the price of a call option on the same stock with the same exercise price and the same expiration date? Explain the reasoning behind your calculations.arrow_forward
- Consider a put option on a stock that currently sells for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (b) Calculate the value of the put option by using first principles (No Arbitrage prin- ciples). Explain the reasoning behind your calculations.arrow_forwardA call option has X=$52 and expire in 360 days (suppose we have 360 days in one year). The risk-free rate is 4%. The call is priced at $11. A put option has X-$52 and is priced at $1. The underlying asset is priced at S0=$43. Suppose in our investments, we could involve one call, one put, one bond, and on stock. How much arbitrage profit could we possibly obtain?arrow_forwardCompute the Black-Scholes price of a call option on a stock which does not pay dividends and has the volatility 0.3, if its exercise price is 200 USD and expiration in two year. Interest rate is zero and the price of the stock is 180 USDarrow_forward
- Compute the Black-Scholes price of a put option on a stock which does not pay dividends and has the volatility 0.3, if its exercise price is 200 USD and expiration in two year. Interest rate is zero and the price of the stock is 180 USD.arrow_forwardNeed helparrow_forwardSuppose XYZ stock pays no dividends and has a current price of $50. The forward price for delivery in 1 year is $55. Suppose the 1-year eective annual interest rate is 10%. (a) Graph the payo and prot diagrams for a forward contract on XYZ stock with a forward price of $55. (b) Is there any advantage to investing in the stock or the forward contract? Why? (c) Suppose XYZ paid a dividend of $2 per year and everything else stayed the same. Now is there any advantage to investing in the stock or the forward contract? Why?arrow_forward
- Imagine all investors are risk-neutral and we have the following binomial tree: 0 Stock: So= 80 1 100 72 2 120 90 86.4 64.8 Using the risk-neutral option valuation approach, calculate the price of a two-year put option on this stock with a strike price $92. Assume that the risk-free rate is 3% per year. Also assume the stock does not pay a dividend. Pick the closest number.arrow_forward(b) Consider two options on the same stock and same time to maturity but with different strike prices. For option A, the strike price (K1) is equal to 10 USD, while for option B, the strike price (K2) is equal to 9.5 USD. The current stock price (S) is equal to 10 USD. There are no dividends and the risk - free is 3% p.a. In calculating the arbitrage - free option prices an investor's volatility estimate is 15% p.a. Yet option A trades for 0.8 USD and option B for 1 USD. i. Compare the implied volatilities of both options A and B to the investor's estimate of 15% ii. ii. Identify the optimal strategy in the two options. Using the investor's volatility estimate, derive the delta - neutral position of your call option portfolio.arrow_forwardSuppose you are a seller . At time t = 0 you get £C from the buyer where C is the risk-neutral price of the option. You then have to design a hedging strategy which would allow you to meet your financial obligation in one year’s time. Your portfolio should consist of two investments: you are allowed to buy the underlying shares and to deposit money in the bank. The price of the share evolves according to a geometric Brownian motion. State the formulae you will need to compute the number of shares in the portfolio and the capital deposited in the bank at any time t, 0 ≤ t ≤ 1.arrow_forward
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