Assume we are in a Black-Scholes world where on day t = 0 a stock is...
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Assume we are in a Black-Scholes world where on day t = 0 a stock is trading at So = $35 per share. The stock price volatility is σ = 25% and it pays a continuous dividend yield D=2%. Suppose the writer of a European option sells a call option with strike K = $33 on 1000 shares with time to expiration T = 180 days. Given risk-free interest rate r = 5% per annum, calculate the following (a) (10p) The call price and the corresponding delta at day 0. (b) (10p) The writer's trading strategy to maintain a delta-hedged portfolio on day 0. How much money does the writer need to borrow/put in a risk-free money market on day 0 in order to maintain a delta-hedged portfolio? (c) (10p) The writer's profit if the stock price increases to $35.50 on day 1. Calculate also the cost to keep the portfolio delta neutral. (d) (10p) The writer's profit if the stock price falls to $34.80 on day 2. Calculate also the cost to keep the portfolio delta neutral. Note if Z N(0, 1), then the cumulative standard normal distribution function in the >0 can be approximated by range [0, ], P(0 <Z<x)=√(2 1 0 < x ≤1. 6 40 336 3456 Assume we are in a Black-Scholes world where on day t = 0 a stock is trading at So = $35 per share. The stock price volatility is σ = 25% and it pays a continuous dividend yield D=2%. Suppose the writer of a European option sells a call option with strike K = $33 on 1000 shares with time to expiration T = 180 days. Given risk-free interest rate r = 5% per annum, calculate the following (a) (10p) The call price and the corresponding delta at day 0. (b) (10p) The writer's trading strategy to maintain a delta-hedged portfolio on day 0. How much money does the writer need to borrow/put in a risk-free money market on day 0 in order to maintain a delta-hedged portfolio? (c) (10p) The writer's profit if the stock price increases to $35.50 on day 1. Calculate also the cost to keep the portfolio delta neutral. (d) (10p) The writer's profit if the stock price falls to $34.80 on day 2. Calculate also the cost to keep the portfolio delta neutral. Note if Z N(0, 1), then the cumulative standard normal distribution function in the >0 can be approximated by range [0, ], P(0 <Z<x)=√(2 1 0 < x ≤1. 6 40 336 3456
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BlackScholes Model Calculations a Call Price and Delta at Day 0 We cant directly calculate the call price and delta without the BlackScholes formula However we can define the parameters needed for the ... View the full answer
Related Book For
Entrepreneurial Finance
ISBN: 978-0538478151
4th edition
Authors: J . chris leach, Ronald w. melicher
Posted Date:
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