IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model
A share follows GBM with S_0 = 100, mu = 10% p.a. and sigma = 30% p.a. What is the median of S_1 (the value exceeded with probability 50%), to the nearest rupee?
The median equals S_0 times e to the power (mu minus sigma squared over 2) times t, which is 100 times e to the power 0.055, about Rs 106. It lies below the mean of Rs 110.5 because of lognormal skewness.
- ARs 111
- BRs 106Correct
- CRs 110
- DRs 115
- Rs 100
Explanation
ln S_1 is normal with mean ln100 + (0.10 - 0.045) = ln100 + 0.055. The median is 100 e^{0.055} = 105.65, about Rs 106. Rs 110 uses the mean e^{0.10} ignoring the Ito term, and Rs 111 is the same figure rounded up from 110.52.
Did you get it right without looking?
One question tells you little. A timed set on Black-Scholes derivative-pricing model shows your real accuracy, how long you take and where you lose marks.
More Black-Scholes derivative-pricing model questions
- Under the Black-Scholes assumptions, which feature of GBM makes it a suitable model for share prices compared with arithmetic Brownian motio…
- A bank has sold 1,000 European call options on a non-dividend-paying share, each on one share. The call delta is 0.60. To be delta-neutral, …
- In deriving the Black-Scholes PDE for a derivative value V(S,t) on a non-dividend-paying share, a portfolio holds one derivative and -Delta …
- For a European put on a non-dividend-paying share in the Black-Scholes model, the put price is P = K·e^(−rT)·N(−d2) − S·N(−d1). An analyst h…
- A trader computes the implied volatility of an at-the-money option using Black-Scholes and finds it exceeds the share's recent historical vo…
- A European call option is written on a share that pays a continuous dividend yield q. Under the Black-Scholes framework, which adjustment gi…