Chapter 16: Option Valuation Flashcards
What is the intrinsic value of an option?
The value an in-the-money call option would have if it were about to expire. The value is S(0) - X.
Intrinsic value for at-the-money or out-of-the-money options is set to 0.
What is the time value of an option?
The difference between an option’s price and its intrinsic value. Be careful with this terminology - this is not the same as the time value of money.
What are the 6 factors that affect the value of a call option?
The stock price, the exercise price, the volatility of the stock price, the time to expiration, the interest rate, and the dividend rate of the stock.
A call’s value should increase with the stock price and decrease with the exercise price because its payoff, if exercised, = S(t)-X.
Volatility of the underlying stock price also tends to increase the value of call options.
Longer time to expiration also tends to increase the value of the call option (more time for an unpredictable event to change value).
Finally, the firm’s dividend payout
What is Two-State Option Pricing?
In order to understand some of the complex math behind options, it is necessary to assume that there are only 2 possible outcomes: a set increase or a set decrease.
What is the Black-Scholes (-Merton) pricing formula?
A formula to value an option that uses the stock price, the risk-free interest rate, the time to expiration, and the standard deviation of the stock return.
C₀ = S₀e^ᵟᵀ(N)(d₁)-Xe^ʳᵀ(N)(d₂)
Where,
d₁=[ln(S₀/X) + (r - δ + 𝜎²/2)T]/𝜎√T
d₂=d₁ - 𝜎√T
Where,
C₀ = current call option value
S₀ = current stock price
N(d) = The probability that a random draw from a std normal distribution will be less than d.
X = exercise price
e = The base of the natural log function, approx 2.71828.
δ = Annual dividend yield of underlying stock.
r = risk-free rate
T = time remaining until expiration
ln = Natural logarithm function.
𝜎 = Standard deviation of the annualised continuously compounded rate of return of the stock, expressed as a decimal, not a percent.
What are the three assumptions underlying the Black-Scholes formula?
- The stock will pay a constant, continuous dividend yield until the option expiration date.
- Both the interest rate, r, and variance rate, 𝜎², of the stock are constant (or in slightly more general versions of the formula, both are known functions of time, so any changes are perfectly predictable)
- Stock prices are continuous, meaning that sudden extreme jumps, such as those in the aftermath of an announcement of a takeover attempt, are ruled out.
What input to the Black-Scholes formula is trickiest and why?
The final input, standard deviation, is not directly observable. It must be estimated from historical data, from scenario analysis, or from the prices of other options, as we will describe momentarily.
Many market participants will ask the question another way: what standard deviation is necessary for the option price that I actually observe to be consistent with Black-Scholes?
