ch15 The Black Scholes merton model Flashcards
What decides the expected return?
The expected return, μ, required by investors from a stock depends on the riskiness of the stock. The higher the risk, the higher the expected return. It also depends on the level of interest rates in the economy. The higher the level of interest rates, the higher the expected return required on any given stock.
What is volatility?
The volatility, σ, of a stock is a measure of our uncertainty about the returns provided by the stock. Stocks typically have a volatility between 15% and 60%.
If volatilities were constant, the accuracy of an estimate would increase as n increased. However, data that is too old may not be relevant to current market conditions. A compromise that seems to work reasonably well is to use
90 to 180 days of data. An alternative rule of thumb is to set n equal to the number of days to which the volatility is to be applied.
Assumptions for Black–Scholes–Merton
1.The stock price follows the process developed in Chapter 14 with μ and σ constant.
2. The short selling of securities with full use of proceeds is permitted.
3. There are no transaction costs or taxes. All securities are perfectly divisible.
4. There are no dividends during the life of the derivative.
5. There are no riskless arbitrage opportunities.
6. Security trading is continuous.
7. The risk-free rate of interest, r, is constant and the same for all maturities.
What is N(d2)?
Probability of excercise
What is K
Strike price
How can European options be analyzed?
European options can be analyzed by assuming that the stock price is the sum of two components: a riskless component that corresponds to the known dividends during the life of the option and a risky component. The riskless component, at any given time, is the present value of all the dividends during the life of the option discounted from the ex-dividend dates to the present at the risk-free rate. By the time the option matures, the dividends will have been paid and the riskless component will no longer exist.
What is Black’s approximation?
Black suggests an approximate procedure for taking account of early exercise in call options.This involves calculating, as described earlier in this section, the prices of European options that mature at times T and tn, and then setting the American price equal to the greater of the two. This is an approximation because it ineffect assumes the option holder has to decide at time zero whether the option will be exercised at time T or tn.
What is the Black-Scholes-Merton model
The Black-Scholes-Merton model is a mathematical formula used to price European call and put options, taking into account factors such as the underlying asset price, strike price, time to expiration, risk-free interest rate, and volatility.
What is the underlying assumption of the Black-Scholes-Merton model?
The underlying assumption of the Black-Scholes-Merton model is that the underlying asset price follows a geometric Brownian motion, which means that the price changes are random and normally distributed.
What is the Black-Scholes-Merton equation?
The Black-Scholes-Merton equation is a partial differential equation used to derive the price of a European call or put option, based on the input variables of the model.
What is the significance of the Greek letters in options pricing?
The Greek letters in options pricing (such as delta, gamma, theta, and vega) represent measures of sensitivity of the option price to changes in the underlying asset price, volatility, time to expiration, and other factors.
What is delta hedging?
Delta hedging is a trading strategy used to reduce or eliminate the risk of an option position by taking offsetting positions in the underlying asset, with the goal of maintaining a neutral overall position with respect to small changes in the underlying asset price.
What is implied volatility?
Implied volatility is a measure of the market’s expectation for the future volatility of an underlying asset, as implied by the current market price of options on that asset.
What is a put-call parity?
Put-call parity is a relationship between the prices of put and call options on the same underlying asset, strike price, and expiration date, that must hold in an efficient market.
