Real Option

# Real Option - FINA537 Equity Valuation Professor Laura...

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1 FINA537 Equity Valuation Professor Laura Xiaolei Liu Real Options

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2 What is Option? • An option is the right, but not the obligation, to do something or receive something in future • Since the holder of the option has the right to make a decision, the option has value
3 An Option Example • Current stock price is \$20, it may go up 10% to \$22 with 80% probability next year, or go down 10% to \$18 with 20% probability, risk free rate is 5% What is the value of a call option, which allows you to buy a stock next year at price \$21?

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4 Option value: Replicating portfolios method • Option payoff: \$1 at good state \$0 at bad state • Form a portfolio, with Δ units of stocks and B units of bond (risk free assets) so that the portfolio have the same payoff as the option at both states Δ *22+B*(1+5%)=1 Δ *18+B*(1+5%)=0
5 Option example: Answer • Two equations with two unknowns, solve for Δ and B Δ =0.25 B=-18/4.2 • Since the portfolio and the option have the same payoffs at both states, they have to have the same price. Option value=0.25*20-18/4.2*1=0.714

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6 Understand the terminology • Exercise price: (K) \$21 • Maturity: (T) 1 year •S t o c k p r i c e : ( S ) \$ 2 0 • Volatility of underlying stock ( σ , range of 22-18) •O p t i o n t y p e : ¾ Call v.s. Put ¾ European v.s. American Option
7 Terminology • Increase %: u=22/20=1.1 • Decrease %: d=18/20=0.9 • Option value in good state: f u =1 • Option value in bad state: f d =0

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8 General formula for option pricing Option value: ) )( 1 ( ) ( d u r d f u f B d u S f f u d d u + = = Δ + + + + = + + + = + + d u d u u d d u f d u u r f d u d r r d u r u r f d r f d u r d f u f S d u S f f ) 1 ( 1 1 1 ) )( 1 ( ) 1 ( ) 1 ( 1 * ) )( 1 ( * ) ( d u f r B Sd f r B Su = + + Δ = + + Δ ) 1 ( ) 1 (
9 Real Option – Option value P=(1+r f -d) ----Risk neutral probability (u-d) Option value = f u ×P+f d ×(1-P) (1+r f )

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10 Option example: double check • u=22/20=1.1 d=18/20=0.9 • P= (1+0.05-0.9) = 0.75 (1.1-0.9) • Option value = 1*0.75+0*0.25=0.714 (1+0.05)
Two-step option value • What is the value of a call option, which allows you to buy a stock two years from now at price \$21? Assuming in the second year, the

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Real Option - FINA537 Equity Valuation Professor Laura...

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