Difficutl CRR /BS and Maringale questions Flashcards
(13 cards)
State prices are always positive in an arbitrage-free market.
Answer: True
→ Negative state prices would imply arbitrage (e.g., getting paid today to deliver nothing in any state).
The sum of risk-neutral probabilities is always equal to 1, regardless of the risk-free rate.
Answer: True
→ Risk-neutral probabilities form a probability distribution over future states.
The sum of state prices equals 1 when the risk-free rate is zero.
Answer: True
→ With 𝑟 =0, no discounting → present value of 1 unit future payoff is 1 → sum of state prices = 1.
Martingale probabilities always reflect real-world likelihoods of events.
Answer: False
→ Martingale (risk-neutral) probabilities are artificial, used for pricing; they adjust for risk preferences, not real-world frequencies.
If state prices increase, option prices increase as well
Answer: True
→ State prices are the building blocks of option values → higher state prices raise the value of contingent claims.
In the Black-Scholes model, asset prices are normally distributed.
Answer: False
→ Returns are normally distributed; prices are lognormally distributed.
In Black-Scholes, increasing volatility increases both call and put option values.
Answer: True
→ More uncertainty → higher value of optionality for both calls and puts.
The Black-Scholes model assumes constant volatility over the option’s lifetime.
Answer: True
→ Constant σ is a key assumption (even if unrealistic).
The up and down factors in the CRR model are chosen so that the expected return equals the market’s risk premium.
Answer: False
→ CRR models use the risk-free rate in risk-neutral valuation, not the market’s risk premium.
In a one-step CRR model, the risk-neutral probability is always between 0 and 1 if there is no arbitrage.
Answer: True
→ If risk-neutral probability leaves [0,1], the tree violates no-arbitrage conditions.
In the Black-Scholes model, the strike price is discounted by the risk-free rate because the payment occurs at maturity.
Answer: True
→ The present value of the strike payment at time T is discounted:
K⋅e −rT
.
The risk-neutral probability in Black-Scholes is a constant value of 0.5.
Answer: False
→ Risk-neutral probabilities depend on
σ, and T; not fixed at 0.5.
In the CRR model, a higher number of time steps leads to a better approximation but increases computational complexity.
Answer: True
→ More steps → closer to continuous model but computationally heavier.
