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Consider a binomial model. The current value of a stock is $70 and the strike price for a put option is $67. The up factor is equal to 1.10 and the...

1.    Consider a binomial model. The current value of a stock is $70 and the strike price for a put option is $67. The up factor is equal to 1.10 and the down factor is equal to 0.80. The risk-free rate is 5%. What is the value of the put option?

2.    Use the Black-Scholes formula to find the value of a call option on the following stock: T = 6 months; σ = 50%; X = 50; S0 = 50; rf = 3%.

3.    A call option with X = 50 on a stock currently priced at 55 is selling for 10. Using a volatility estimate of 30%, you find that N(d1) = 0.6 and N(d2) = 0.5. The risk-free rate is 0%. Is the implied volatility more or less than 30%? Explain.

4.    A delta-neutral portfolio is hedged against:

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