# Fins3635 Final Essay

933 Words
Sep 25th, 2013
4 Pages

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

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

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Also, X3 > X2 > X1 and X3 − X2 = X2 − X1 . All options have the same maturity. Show that: c2 < 0.5(c1 + c3 ). (b) A portfolio comprises of a long position in straddle spread with strike of $5 and a strangle spread with strikes spread by $3 around this central position. • • • • Draw the payoﬀ diagram of the total portfolio and each position. Comment on the delta, gamma, and theta of the straddle spread. Comment on the delta, gamma, and theta of the strangle spread. Describe some possible uses of the combined portfolio.

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4) (a) The Binomial model for option pricing and the Black-Scholes model are both based on risk-neutral pricing. Explain why the two models don’t necessarily yield the same option price. (b) Explain, without references to pricing formulas, why each of the following statements is correct for a long European call option on a stock: • The delta of a call option is always positive. • The delta of a call option is highest when the option is in the money. • The theta of a call option is always negative. (c) The current stock price is S. In one time period the stock price will be Su or Sd , where Su > Sd . The payoﬀ from a call option at time T is the max (ST − K, 0), where K is the exercise price. Assume the current risk-free rate is r. • What is the value of the option if K > Su ? • What is the value of the option if K < Sd ?

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5) In a wind farm, wind turbines generate electricity from the force of

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4) (a) The Binomial model for option pricing and the Black-Scholes model are both based on risk-neutral pricing. Explain why the two models don’t necessarily yield the same option price. (b) Explain, without references to pricing formulas, why each of the following statements is correct for a long European call option on a stock: • The delta of a call option is always positive. • The delta of a call option is highest when the option is in the money. • The theta of a call option is always negative. (c) The current stock price is S. In one time period the stock price will be Su or Sd , where Su > Sd . The payoﬀ from a call option at time T is the max (ST − K, 0), where K is the exercise price. Assume the current risk-free rate is r. • What is the value of the option if K > Su ? • What is the value of the option if K < Sd ?

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5) In a wind farm, wind turbines generate electricity from the force of