Risk Management: Binomial Option Pricing Model

Binomial Option Pricing Model

• The Binomial Option Pricing Model is a financial model used to determine the theoretical value of options using a simplified approach.
• It represents the possible price paths that an underlying asset might take over time.
• The model divides the time to expiration into potentially numerous steps or intervals, with the price of the underlying asset moving up or down by a specific factor at each interval.
• The binomial model is particularly useful because it can be applied to options that have various features and exercise rules, such as American options.

Steps of Binomial Model

• Step 1: Create the binomial tree
• Step 2: Expand the binomial tree
• Step 3: Calculate the option payoff at expiration
• Step 4: Work backwards to calculate the option price

One-Period Binomial Model

• The time to expiration of the option is divided into just one interval.

Two-Period Binomial Model

• The time to expiration is split into two intervals.
• The stock price can either move up or down by a specific factor at the end of the period.

Calculating Binomial Model

• Calculate the possible future values of the stock (S_u and S_d)
• Calculate the option values at the end of the period (C_u and C_d)
• Calculate the risk-neutral probability (p) of the stock moving up
• Calculate the present value of the expected option payoff (C)

Options

• Buying a call option grants the buyer the right to buy the underlying asset at a specified price (strike price) before the option expires.
• Writing a call option involves the seller granting the buyer the right to purchase the underlying asset at a specified price.
• Buying a put option gives the buyer the right to sell the underlying asset at a predetermined price before the option expires.
• Writing a put option means the seller grants the buyer the right to sell the underlying asset at a specified price.

Options Strategies

• Covered calls: holding a long position in an asset while selling call options on the same asset to generate income from the option premiums.
• Protective put: buying put options for an asset that one already owns to hedge against potential losses in the asset's value.

Hedge Portfolio

• A hedge portfolio offers several benefits, primarily centered around risk management and return stability.
• Key advantages of maintaining a hedge portfolio:
  • Risk reduction
  • Diversification
  • Protection against market volatility

Interest Rate Forwards and Options

• Forwards contractually lock in future interest rates for borrowing or lending.
• Options provide the right, but not the obligation, to enter into such transactions at predetermined rates.
• Forward rate agreements (FRA) are forward contracts in which the underlying is an interest rate.

Forward Rate Agreements

• A company enters into a forward rate agreement (FRA) to hedge against interest rate fluctuations.
• The FRA is based on a contract period, notional amount, and agreed upon fixed rate.
• The payoff of the FRA is calculated based on the LIBOR rate at the time of settlement.