I only need help with number #4 (files attach should help)

1. For the following questions, assume a stock is priced according to a geometric Brownian motion process

Δ = Δ + √Δ

where = 0.10, = 0.15, Δ = 1/52, and is a random draw from a standard normal pdf. Additionally, assume that the initial stock value, 0 = 80 and that the derivatives that follow expire in 26 weeks ( = 1/2). Also, assume that implied volatility every week is 0.30 and the risk-free interest rate is equal to 0.02.

- Simulate a single price trajectory using the information above.
*Note: Make sure to set a seed in simulations to ensure consistency through repeated**simulations*. - Compute the implied call option premium for every week, with K=85, using theinformation from above and simulated values from part (a).
- Assume you are looking to sell 10 European call options at t=0 and opt to use a deltahedge throughout the life of the option.
- Derive the delta associated with each week.
- Derive the number of long futures contract you would use to hedge each week.

- Simulate 1,000 price trajectories using the information above.
*Note: Make sure to set a seed in simulations to ensure consistency through repeated simulations*.- Using the simulated outcomes from above, compute the associated returns from a type of Asian put and an Asian call option where the payment is equal to the difference between the average price of the last 5 weeks of the stock and the strike, K.
- Using the simulated outcomes from above, compute the associated returns from an all-or-nothing option that pays $100 when ≥ 95 at any time during the life of the contract.
- Using the simulated outcomes from above, compute the associated returns from a floating call price, where K=85 and the price is the maximum of all prices within the life of the contract.
- Using the simulated outcomes from above, compute the associated returns from a floating put price, where K=85 and the price is the minimum of all prices within the life of the contract.

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