Semi Fi: G6: Financial Option Valuation Techniques Flashcards
1997 Nobel Prize (Black-Scholes Option Pricing Model)
Robert Merton
Myron Scholes
Fischer Black
Common techniques, derived from black and scholes’ insights
Black-Scholes option pricing model
Binomial option pricing model
Risk-neutral probabilities
Risk and return of an option
Corporate applications of option pricing
Gives holder the right (but not the obligation) to purchase an asset at some future date
Call option
Gives the holder the right to sell an asset at some future date
Put option
The price at which the holder agrees to buy or sell the share of stock when the option is exercised
Strike price or exercise price
The last date on which the holder has the right to exercise the option
Expiration date
Can be exercised on any date up to, and including the exercise date
American option
Can be exercised only on the expiration date
European option
It can be derived from the binomial option pricing model by making the length of each period, and the movement of the stock price per period, shrink to zero and letting the number of periods grow infinitely large
Black-Scholes option pricing model
Five input parameters to price the call
Stock price
Strike price
Exercise date
Risk-free rate
Volatility of the stock
An option can be valued using a portfolio that replicates the payoffs of the option in different states
Binomial option pricing model
It assumes two possible states for the next time period, Given today’s state.
Binomial option pricing model
The value of an option is the value of the portfolio that replicates it’s payoffs. The replicating portfolio will hold the underlying asset and risk free debt, and will need to be rebalanced overtime.
Binomial option pricing model
A portfolio of other securities that has exactly the same value in one period as the option.
Two-state single-period model
There are more than two possible outcomes for the stock price in the real world
Multiperiod Model
Also known as state-contingent prices, state prices, or Martingale prices
Risk-neutral probabilities
Probabilities under which the expected return of all securities equals the risk free rate. These probabilities can be used to price any other asset for which the beat of in each state are known.
Risk-neutral probabilities
In a binomial tree, the risk-neutral probability p that the stock price will increase is given by
Risk-neutral probabilities
Risk-neutral probabilities formula
P = (1 + rf ) x S - Sd
Divide by Su - Sd
Any security whose pay-off depends solely on the prices of other marketed assets
Derivative security
The basis for a common technique for pricing derivative securities called Monte Carlo simulation
Risk-neutral pricing method
True or false
In the randomization, the risk-neutral probabilities are used, and so the average payoff can be discounted at the risk-free rate to estimate the derivative security’s value
True
Probability call option formula
Pc = P x (Su - K )
Divide by (1 + rf )
Probability put option formula
Pp = P x (K - Sd)
Divide by (1 + rf )
True or false
The beta of an option can also be calculated by completing the beta of its replicating portfolio
True
For stocks with positive betas, calls will have larger betas than the underlying stock, while puts will have negative betas. The magnitude of the option bed that is higher for options that are further out of the money.
Risk and return of an option
True or false
For stocks with negative betas, calls will have larger Betas than the underlying stock, while puts will have negative betas.
False
As the stock price changes, the beta of an option will change
Risk and return of an option
Two corporate applications of option pricing
- Unleveraging the beta of equity, and calculating the beta of a risky debt
- Deriving the approximation formula to value debt overhang
True or false
When debt is risky, the betas of equity and debt increase with leverage
True
True or false
When debt is risky, the betas of equity and debt decrease with leverage
False
Uses of option pricing methods
Assess potential investment distortions that might arise due to debt overhang or the incentive for asset substitution and risk-taking
Evaluate state–contingent costs, such as financial distress costs
Enhance the value of the firm
