Let h = 1/52. Simulate both the continuously compounded actual return and the actual stock price, St+h. What are the mean, standard deviation, skewness, and kurtosis of both the continuously compounded return on the stock and the stock price? Use the same random normal numbers and repeat for h = 1. Do any of your answers change? Why?
Answer to relevant QuestionsAn options trader purchases 1000 1-year at-the-money calls on a non-dividend paying stock with S0 = $100, α = 0.20, and σ = 0.25. Assume the options are priced according to the Black-Scholes formula and r = 0.05. a. Use ...Let ui ∼ U (0, 1). Compute _12 i=1 ui − 6, 1000 times. (This will use 12,000 random numbers.) Construct a histogram and compare it to a theoretical standard normal density. What are the mean and standard deviation? (This ...Suppose that on any given day the annualized continuously compounded stock return has a volatility of either 15%, with a probability of 80%, or 30%, with a probability of 20%. This is a mixture of normals model. Simulate the ...Use Itˆo’s Lemma to evaluate dS−1. For the following four problems, use Itˆo’s Lemma to determine the process followed by the specified equation, assuming that S(t) follows (a) Arithmetic Brownian motion, equation ...What is the value of a claim paying Q(T )2S(T )? Check your answer using Proposition 20.4.
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