Morgan Stanley Quant Onsite 面经

Round 1:
1.1 What is the fair value of a future with maturity T and constant interest rate r? If the price is great than the fair value, what is your strategy to make money?
1.2 European call options of two models: (1) Black-Scholes model: interest rate r and volatility σ are constant (2) in addition to Brownian motion with same parameters r, σ, the price of the stock has a jump θ with probability λdt in the interval [t, t + dt), where θ, λ are positive constants. Which call option has higher price?

Round 2:
2.1 X, Y are independent random variables with normal distribution N (0, 1). How do you construct a new random vari

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How do you represent P (A) in terms of an expectation?
4.3 What is the definition of Brownian motion W(t)? Can you find an upper bound b such that |W(t)| ≤ b(∀0 ≤ t ≤ 1)? What is the definition of Martingale M(t)? Given M(0) = 0 and |M(t)| = 1 almost surely, can you find an upper bound b such that |M(t)| ≤ b(∀0 ≤ t ≤ 1)?

1.2怎么做呀字数字数字数

1.2和4.1都是不错的题，感谢分享