# Black-Scholes-Merton Model and the Greeks

The Black-Scholes-Merton model has six inputs (or five, if gamma is considered a sub-part of delta); five are known as the Greeks.

**Delta:**The change in the option price per one dollar change in the underlying stock's price; alternatively, the change in the option price equals the change in the underlying multiplied by the option's delta.**Gamma:**The sensitivity of delta to the change in a price of the underlying asset.**Theta:**An option's price is affected by the amount of time to expiration; the longer the time, the more valuable the option. Theta is a measure of the rate of the time value decay of the option.**Rho:**This is an option's price sensitivity to a change in the risk free rate. Rho is commonly small and a European option's price is not heavily sensitive to a change in the interest rate.**Vega:**This is volatility sensitivity; specifically vega is option price sensitivity to the standard deviation of the asset's return. As volatility increases, options become more valuable.**Strike (or Exercise) Price:**This is the price at which the underlying asset can be bought (long call) or sold (long put) by the option holder. Excluding other factors, as strike prices go up calls are worth less and puts are worth more.

Summary of Input Impacts on Option Prices:

INCREASE TO | CALL PRICE | PUT PRICE |
---|---|---|

Dividend | Down | Up |

Interest Rates | Up | Down |

Volatility | Up | Up |

Underlying Asset Price | Up | Down |

Time to Expiration | Up | Up |

Exercise/Strike Price | Down | Up |

LESSONS

- CFA Level 2: Derivatives Part 2 – Introduction
- Introduction to Options
- Synthetic Options and Rationale
- One Period Binomial Option Pricing Model
- Call Option Price Formula
- Binomial Interest Rate Options Pricing
- Black-Scholes-Merton (BSM) Option Pricing Model
- Black-Scholes-Merton Model and the Greeks
- Dynamic Delta Hedging & Gamma Related Issues
- Estimating Volatility for Option Pricing
- Put-Call Parity for Options on Forwards
- Introduction to Swaps
- Plain Vanilla Interest Rate Swap
- Equity Swaps
- Currency Swaps
- Swap Pricing vs. Swap Valuing
- Pricing and Valuing a Plain Vanilla Interest Rate Swap
- Pricing and Valuing Currency Swaps
- Pricing and Valuing Equity Swaps
- Swaps as Theoretical Equivalents of Other Derivatives
- Swaptions and their Valuation
- Swap Credit Risk and Swap Spread
- Interest Rate Derivatives - Caps and Floors
- Credit Default Swaps (CDS)
- Credit Derivative Trading Strategies

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