- 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

# Dynamic Delta Hedging & Gamma Related Issues

- Traders and securities dealers can use an option's delta to create hedges for the price risk exposure that they have in other option or underlying asset positions.

Example, assume that a securities dealer has sold (short position) 100 call options on Ford Motors (NYSE: F) and that each option represents 100 shares. Thus, the dealer's net stock exposure is 10,000 shares. If the options on F have a delta of 0.8, then the dealer can counter his short call position by buying 8,000 shares of F. Thus if the stock increases by $1, the increase in the value of the long stock position should offset the loss on the short call option position.

Delta is dynamic, though, and will change as the underlying asset price changes. Therefore delta hedging requires constant readjustment.

Because of this, delta hedging is also called

*dynamic hedging*.

Delta hedging loses its effectiveness when an underlying asset has large price moves, either up or down.

As previously discussed, gamma represents the sensitivity of delta to a change in the underlying asset's price.

When an option is either deep in or deep out of the money, gamma will be close to zero as it will take a large price move to impact the value of delta; an option's gamma is comparable to a bond's convexity.

When an option is at the money and expiration is close, then gamma tends to be high.

When gamma is high, delta becomes a less accurate measure of option price sensitivity to the underlying asset and delta hedging loses accuracy as a hedging technique.

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