Manual American-Style Derivatives: Valuation and Computation

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Similarly, the more volatile the underlying asset, the greater the odds that it will expire ITM. Higher interest rates should translate into higher option prices.

American-Style Derivatives: Valuation and Computation

Real traded options prices are determined in the open market and, as with all assets, the value can differ from a theoretical value. However, having the theoretical value allows traders to assess the likelihood of profiting from trading those options. The evolution of the modern-day options market is attributed to the pricing model published by Fischer Black and Myron Scholes. The Black-Scholes formula is used to derive a theoretical price for financial instruments with a known expiration date.

However, this is not the only model. The Cox, Ross, and Rubinstein binomial options pricing model and Monte-Carlo simulation are also widely used.

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The original Black-Scholes model required five input variables - strike price of an option, current price of the stock, time to expiration, risk-free rate , and volatility. Also, implied volatility is not the same as historical or realized volatility.

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Currently, dividends are often used as a sixth input. Additionally, the Black-Scholes model assumes stock prices follow a log-normal distribution because asset prices cannot be negative. Other assumptions made by the model are that there are no transaction costs or taxes, that the risk-free interest rate is constant for all maturities , that short selling of securities with use of proceeds is permitted, and that there are no arbitrage opportunities without risk.

Clearly, some of these assumptions do not hold true all of the time.

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American-style derivatives. Valuation and computation - PDF Free Download

For example, the model also assumes volatility remains constant over the option's lifespan. This is unrealistic, and normally not the case, because volatility fluctuates with the level of supply and demand. However, for practical purposes, this is one of the most highly regarded pricing models.


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Pricing American Derivatives using Simulation: A Biased Low Approach

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Personal Finance. How the theoretical value may vary with changes to the input variables can also be found. Please note that this calculator is an educational tool intended to help individuals learn how options and warrants work.

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The actual market environment may not be the same as what the theoretical models assume. Users of this calculator should not make investment decisions based upon values generated by it only.

2015- CFA level I- Basic of Derivative Pricing and Valuation- Part I (of 4)

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