A stock is at $400 with a volatility of 0.35. The interest r…

A stock is at $400 with a volatility of 0.35. The interest rate is 6%. Simulate 20,000 paths using a daily price simulation for 2 years with geometric brownian motion dynamics. Price a 2-year rebate option. The rebate option pays Max(St-410,0) as soon as the stock crosses $450 and nothing otherwise. Note that t is therefore a random stopping time, and not necessarily the time to expiration. Upload code.  

A stock is at $100 and moving with a volatility of 0.40. The…

A stock is at $100 and moving with a volatility of 0.40. The interest rate is 5% per year. Price a derivative that pays at the end of 2 years if there is some time interval during the 2 years where the stock price first reaches $105 and then drops to $95. It pays nothing otherwise. is the price of the stock at expiration in 2 years. Use geometric brownian motion dynamics for the stock. Run 20,000 daily simulations for the 2-year period and find the price of the derivative. Upload code.