FINS 3635 - Options, Futures, and Risk Management Techniques: Mock Final May 28, 2012
1) Consider a ﬁrm with two classes of zero-coupon debt: senior debt and junior debt. Suppose that the ﬁrm’s debt securities both mature at time T1 and the senior ranking debt has a face value of X1 and the junior ranking debt has a face value of X2 . The claims of the senior debt holders are paid ﬁrst, before the claims of the junior debt holders, who in turn are paid out their claims before the equity holders. The equity holders have limited liability. (a) Suppose that the total ﬁrm value at maturity is denoted as VT1 . Find the payoﬀ of the shareholders, the senior debt holders, and the junior debt holders at time T1 . (b) Hence ﬁnd the expressions for the value of the securities issued by the ﬁrm at time 0 to both the equity holders and the debt holders under the standard Black-Scholes framework. (c) Use the following valuation assumptions, compute the value of the senior debt security: • • • • • • • Continuously compounded risk-free rate = 11.3445% Volatility = 19.0620% Dividend yield = 2% Term = 1 year X1 = $90.00 X2 = $10.00 V = $100 = value of ﬁrm’s assets
2) (a) Consider a Bermudan call option over an asset that pays no dividends. Suppose the Bermudan option has exercise price X, a ﬁnal maturity date and one early exercise date. • The payoﬀ at the ﬁnal maturity date T2 is max(ST2 − X, 0). • The option can be exercised early only at time T1 and the payoﬀ at that time would be max(ST1 − X, 0). Using put-call parity for European options, show that it is never optimal to exercise this Bermudan option early. (b) Consider a Bermudan put option over an asset that pays no dividend. Suppose the Bermudan option has exercise price X and ﬁnal maturity date T2 and early exercise date T1 . Using put-call parity, what is the optimal early exercise strategy for this option? (c) Does the optimal early exercise strategy in parts (b) and (c) change if we use a pricing model other...
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