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Valuing Stock Options
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Valuing Stock Options This model, really a template, is used to value European stock opt you can purchase 100 shares of a stock at a given exercise price a the stock price will increase above the exercise price so that you c opposite is true for a put, where you can sell 100 shares of a sto Then you are hoping that the stock price will decrease below the exe low. The model uses the well-known lognormal model of stock price chang C11. This formula depends on the time till expiration, the riskfre well as a standard normal variate. Given this future price, the va calculated in row 15, their discounted values (discounted continuo designated as @RISK outputs in row 16, and the means of these disc According to theory, these means approximate the values of the opt Alternatively, the famous Black-Scholes formula can be used to val simulation. These values are calculated in row 20. When you run th should find that the means from the simulation in row 17 are withi
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Valuing Stock Options excel file
Transcript of Valuing Stock Options
Explanation
Valuing Stock Options
This model, really a template, is used to value European stock options: calls and/or puts. With a call option, you can purchase 100 shares of a stock at a given exercise price at a given expiration date. You are hoping that the stock price will increase above the exercise price so that you can make a profit: buy low, sell high. The opposite is true for a put, where you can sell 100 shares of a stock at the exercise price at the exercise date. Then you are hoping that the stock price will decrease below the exercise price, so that you can sell high, buy low.
The model uses the well-known lognormal model of stock price changes to simulate the future stock price in cell C11. This formula depends on the time till expiration, the riskfree rate, and the volatility of the stock, as well as a standard normal variate. Given this future price, the values of the options, call or put, are calculated in row 15, their discounted values (discounted continuously at the riskfree rate) are calculated and designated as @RISK outputs in row 16, and the means of these discounted values are calculated in row 17. According to theory, these means approximate the values of the options.
Alternatively, the famous Black-Scholes formula can be used to value the options analytically -- without simulation. These values are calculated in row 20. When you run the simulation for, say, 10,000 iterations, you should find that the means from the simulation in row 17 are within a few pennies of the Black-Scholes values.
Model
InputsCurrent stock price$100.00Exercise price$100.00Expiration date (years)0.50Annual volatility20%Annual risk-free rate5%Shares per option100SimulationStock price at expiration$101.51
Outputs and summary measuresCallPutPayoff at expiration$151.13$0.00Discounted payoff$147.40$0.00Mean discounted payoff$688.81$442.00Black-Scholes formulas (analytic, no simulation)Price of optionCallPut$688.87$441.97Parameters for Black-Scholesd10.2475-d1-0.2475d20.1061-d2-0.1061N(d1)0.5977N(-d1)0.4023N(d2)0.5422N(-d2)0.4578
