a Draw 2 period binomial tree of your assets assuming an asset volatility of

A draw 2 period binomial tree of your assets assuming

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(a) Draw 2-period binomial tree of your assets, assuming an asset volatility of 33.65% per year and the risk-free interest of 10% per annum. (b) Will you exercise the option to maintain the assets? 2. EarBook Inc has issued a mandatory zero-coupon convertible bond. EarBook’s asset value today is 100. Each period it can go up by u=1.25 or down by d=1/u. The risk free rate is 5%. (a) Draw the asset value tree of EarBook Inc. (b) The mandatory convertible bond has to be converted into shares either at t=1 or at t=2, which is the maturity date of the convertible. The fraction of shares obtained after conversion is γ . In contrast to normal convertible bonds, γ depends on the value of assets. The following diagram displays the time varying γ of the convertible. γ u = 0 . 07 γ d = 0 . 12 γ uu = 0 . 06 γ ud = 0 . 10 γ dd = 0 . 14 t = 0 t = 1 t = 2 1
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What is the market value of this mandatory convertible bond today? 3. Use the put-call parity to derive, for a non-dividend paying stock, relationship between: (a) The delta of a European call and the delta of a European put (b) The gamma of a European call and the gamma of a European put 4. Show that the delta (Δ), gamma (Γ) and theta (Θ) of a non-dividend paying call option (call value C ) satisfy the following equality: Θ + rS 0 Δ + 1 2 σ 2 S 2 0 Γ = rC Is the equation applicable for non-dividend paying put? 5. A company uses delta hedging to hedge a portfolio of long positions in put and call options on a currency. Which would give the most favorable result for the portfolio (delta hedged): a virtually constant spot rate or wild movements in the spot rate? Explain briefly 2
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