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# lecture13post - Recap Real options Implied volatilities...

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Unformatted text preview: Recap Real options Implied volatilities Lecture 13 - Real options BUSI 588, Fall 2011 Diego Garc a Kenan-Flagler Business School UNC at Chapel Hill October 10th, 2011 c Diego Garc a, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 13 - Real options 1 / 23 Recap Real options Implied volatilities Outline 1 Recap BUSI 588 formulae and concepts Risky debt 2 Real options Motivation Clinton case 3 Implied volatilities VIX Smiles in option markets Handouts today: Class slides, case 13 solutions and 2010 exam solutions. In-class, closed-book exam this Friday, 9am-11.30am. McColl: 3500, 3575 (make-ups in McColl 2000, Monday 8am-10.30am). Office hours almost anytime this week (email). c Diego Garc a, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 13 - Real options 2 / 23 Recap Real options Implied volatilities Formulas in BUSI 588? Payoff from a call: max( S T- K , 0), where S T is the price of the underlying asset at maturity, and K is the strike price. Payoff from a put: max( K- S T , 0). Payoff from a (long) forward: S T- F , where F is the delivery price of the forward contract. Convention on dividends: invest in 1 unit of underlying means we get S T (1 + ) T in T years. Put-call parity: P t = C t- S t (1 + ) T- t + K (1 + r f ) T- t where P t is put price at date t , C t is call price, S t is the underlying asset price, r f is the risk-free rate, is the dividend yield, and T- t is the time to maturity of the options. c Diego Garc a, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 13 - Real options 3 / 23 Recap Real options Implied volatilities Formulas in BUSI 588? Forward price for delivery at date T is F T = S (1 + r f ) T (1 + ) T (1 + c ) T (1 + y ) T where c are storage cost (in annual % terms), and y is the convenience yield. Risk-neutral probability of an up move: p u = r- d u- d Derivative value = Value of the replicating portfolio = S t + Cash position. Squared-root rule for volatlity: a = 12 m , where a is the volatility of annual returns, and m is the volatility of monthly returns. c Diego Garc a, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 13 - Real options 4 / 23 Recap Real options Implied volatilities Formulas in BUSI 588? All the Greeks (but ) satisfy the portfolio property: P = n 1 1 + n 2 2 . Risky debt = Risk-free debt minus a put option on the firms assets with a strike equal to the face value of debt. Equity is a call option with the same strike. D = F (1 + r f ) T- P ( K = F ) A convertible bond is the same but with some call options D C = F (1 + r f ) T- P ( K = F ) + C ( K = F / ) with denoting the fraction of the firm owned by the convertible debt holders upon conversion. c Diego Garc a, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 13 - Real options 5 / 23 Recap Real options Implied volatilities Concepts in BUSI 588 What are calls and puts? What trading strategies can we implement with them?...
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## This note was uploaded on 11/25/2011 for the course BUSI 588 taught by Professor Staff during the Fall '10 term at UNC.

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lecture13post - Recap Real options Implied volatilities...

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