# One Period Binomial Option Pricing Model

- The following model can be used for options on stocks, currencies, and commodities; points on interest rate option pricing will be made at the end of this section.
- A critical component for option pricing with the one period binomial model is the notion of constructing a hedged portfolio.

**H = nS - c**

H = The value of the hedged portfolio

n = Hedge ratio

S = Price of the underlying asset

c = Call price

A hedged portfolio will be "riskless" in that there is a perfect balance between a long position in the underlying and a short position in the call, so the gain in one offsets the loss to the other.

**n = (c+ - c-)/(S+ - S-)**

- c+ = The price of the call when the underlying rises to S+
- c- = The price of the call with the underlying falls to S- Note that these values are "intrinsic" values (difference between the underlying's future price and the option's strike price). For example, if the strike price is $25/share and the upside is $30/share, then c+ is $5.
- S+ = The upside price of the underlying asset
- S- = The downside price of the underlying asset

Upside and downside for the underlying must be converted to 1 + the % price move

u = (S+/S)

d = (S-/S)

S = Starting price for the underlying

Because the hedged portfolio is a risk free portfolio, the rate of return on the hedged portfolio should equal the risk free rate.

The one period model can be expanded to multiple periods.

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- 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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