Black Scholes Term Paper

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The price of Google today is $520.00 (MSN Moneycentral, 2014). The assumption then is that the strike price is going to be $572. The price of an option is related to the strike price, the price of the stock, the time to expiry, and the volatility of the stock and the risk free rate, according to the Black-Scholes option pricing model (Folger, 2014). The case notes that the option is a call, but does not say anything about expiry. So it is assumed that the option expires in 90 days. The risk free rate, based on the 1 year Treasury, is 0.078%.

The challenge in implementing Black-Scholes is to figure out the implied volatility. There doesn't appear to be a great source for this, but online it seems to be in the 17-18% range for Google, so 17% will be used. The Black-Scholes calculator is used: http://www.mystockoptions.com/black-scholes.cfm

The value of this call option is $3.061, using this formula. A 60-day call with a strike price of $575 currently has a bid-ask of $3.60 - $4.00, so the current findings from the Black-Scholes are not too far off.

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If anything, the Black-Scholes calculation is a little bit low, because the 90-day option is further out than the 60 day that exists on the market. If the implied volatility has increased, for example to 20%, then the Black-Scholes gives us a price of this call of $4.978. It appears, from this analysis, that the call is slightly overpriced in the market, which might mean that Google's implied volatility has increased. Still, it is believed that this option is overpriced, given where Google's volatility appears to be at present.

The futures contract in June 2014 for crude oil is $101.50. A year ago, the one-month futures contract for crude oil was $91.95.

If I had invested $1,000 in that futures contract a year ago, it would be worth $1,103.86., which implies a gain of $103.86.

I would speculate that this will be worth more in the next year. That is mostly based on the expected change in the price of oil. The….....

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