Using Black-Scholes find the price of a European call option on a non-dividend paying stock when the stock price is $69, the strike price is 70, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is three months? What is the value of a put using theses parameters (use put-call parity)? What happens to the price of the call if volatility is 10% and 50%? Show the prices at these volatilites.

Using Black-Scholes find the price of a European call option on a non-dividend paying stock when the stock price is $69, the strike price is 70, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is three months? What is the value of a put using theses parameters (use put-call parity)? What happens to the price of the call if volatility is 10% and 50%? Show the prices at these volatilites.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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A stock price (which pays no dividends) is $48.08 and the strike price of a 2 year European put option is $56.63. The risk-free rate is 4% (continuously compounded). What is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? Use 2 decimal places.
An engineer prepares a report to evaluate a project using PW and IRR. Just before submitting the report, he spills coffee on it, making the first digit of the 2-digit IRR unreadable. The second digit is a 2. The PW is negative and MARR is 15 percent. He doesn’t have time to redo the analysis. Can you help him figure out the IRR?
QUESTION: 2. What is the fair value for a six-month European call option with a strike price of $135 over a stock which is trading at $138.15 and has a volatility of 42.5% when the risk free rate is 1.85% using the two step binomial tree? a) What is the delta of this option? b) What is the probability of an up movement in this stock? c) What is the probability of a down movement in this stock? d) What is the proportional move up for this stock e) What is the proportional move down for this stock f) What would be the value of the put option with the same strike price?
The price S(t) of a share follows the geometric Brownian motion S(t) = Se µt+σW(t) . The price of the share at t = 0 is S = £25 and µ = 0.1. The continuously compounded interest rate is 8%. However, the volatility σ is not known. (a) Explain the definition of implied volatility. (b) A European call option on the above share with the strike price K = £23 and expiration time of 6 months has the market price £3.1. Does the equation defining the implied volatility have a solution? [6] Hint. You are not supposed to solve the equation defining the volatility to answer this question.
D3) 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?
You are pricing options with the following characteristics: •Current stock price (St): $35.60 •Exercise price (X): $50 •Time to expiration (T-t): 9 months •Risk-free rate (rf): 3.25% •Volatility (0): 45% (a): What is the Black-Scholes value of call option? In your hand-written solution, provide the calculations of d1,d2, and the final call price. Use Excel or another spreadsheet program to compute the values of N(d1) and N(d2). See the notes for details. (b): Using put-call parity, what is the value of a put option? For this case, assume continuous compounding, which implies that PVt(X)=e-r(T-t).X.
Given the following information, predict the put option's new price after the stock's volatility changes. Initial put option price = $6 Initial volatility = 25% Vega = 13 New volatility = 18% (required precision 0.01 +/- 0.01) Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂r
D4) Consider a two-step binomial tree. What is the delta of the put option if: the futures price is S = 1682.00, the risk-free rate is r = 2.90%, the strike price is K = 1757.00, the maturity is T = 12 months and the tree parameters are u = 1.1357 and d = 0.8620? (keep 4 decimals in your calculations).
please answer as soon as possible?
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.
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%
Black-Scholes Model Use the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is $28, (2) strike price is $34, (3) time to expiration is 6 months, (4) annualized risk-free rate is 6%, and (5) variance of stock return is 0.09. Do not round intermediate calculations. Round your answer to the nearest cent. $

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