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Venture Capital and the Finance of Innovation [Course number]

Option Definitions. A European call option gives the holder the right to buy an asset at a preset exercise price on an expiration date.For a put option, just substitute sell" for buy".Strike price" is a synonym for exercise price.For an American option, exercise can occur anytime on or before

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Venture Capital and the Finance of Innovation [Course number]

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    1. Venture Capital and the Finance of Innovation [Course number]

    2. Option Definitions A European call option gives the holder the right to buy an asset at a preset exercise price on an expiration date. For a put option, just substitute “sell” for “buy”. “Strike price” is a synonym for exercise price. For an American option, exercise can occur anytime on or before the expiration date.

    3. Option “Moneyness” If the exercise price is higher, the same, or lower than the current stock price, then we say that a call option is “out-of-the-money”, “at-the-money”, or “in-the-money”, respectively. For put options, reverse this ordering (e.g., put options are out-of-the-money when the exercise price is lower than the current stock price.)

    4. Call Option

    5. Put Option

    6. Example Suppose that Bigco is currently trading for $100 per share. We are offered a European call option to purchase one share with an expiration date in one year. We know that on the expiration date Bigco stock will sell for either $120 per share (a “good day”: probability = 80%) or for $80 per share (a “bad day”: probability = 20%). No other prices are possible. The stock will not pay any dividends during the year. The riskless interest rate is zero, so a bond can be purchased (or sold) for a face value of $100 and have a certain payoff of $100 in one year. Stocks, bonds, and options can all be bought or sold, long and short, without any transactions costs.

    7. Black-Scholes Assumptions “Perfect Markets” that are Open all the time Allow assets to be traded in any quantity No taxes or transactions costs No remaining arbitrage opportunities Technical assumptions about the statistical properties of stock and bond returns. (Most famously, log normal stock returns).

    8. Black-Scholes Formula

    9. EXHIBIT 13.7 – FIVE-YEAR COMPOUND RETURNS FOR A LOGNORMAL DISTRIBUTION

    10. Random-Expiration (RE) Options Continuous-time probability (q) of forced expiration. Expected holding period = H = 1/q

    11. RE Call Formula

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