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IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model

Under the Black-Scholes assumptions, which feature of GBM makes it a suitable model for share prices compared with arithmetic Brownian motion?

GBM keeps share prices positive because they are lognormal, and proportional returns over non-overlapping periods are independent. This fits limited liability and the idea that volatility scales with price level, unlike arithmetic Brownian motion.

  1. APrices can become negative, which reflects limited liability
  2. BExpected price is independent of time
  3. CPrices stay positive and proportional returns over disjoint intervals are independentCorrect
  4. DVolatility of price in rupees is constant regardless of price level
  5. Log returns are perfectly correlated across periods

Explanation

GBM gives lognormal prices that are always positive, and log returns over non-overlapping intervals are independent and normal. Arithmetic Brownian motion allows negative prices and has constant absolute volatility, which options 1 and 4 wrongly attribute to GBM.

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