Assume annual compounding. The one-year and two-year zero-coupon rates in the BDT model are 6% and 7%. The volatility is given to be $\sigma = 0.30$ . What is the price of a one-year maturity floor on the one-year interest rate at a strike rate of 8% and a notional of $100?
A) 1.000
B) 1.026
C) 1.052
D) 1.078

Question

Quizplus · Accepted Answer

A floor on the interest rate is a derivative that pays off when the interest rate falls below a certain level (the strike rate). The payoff is based on the difference between the strike rate and the actual rate, applied to the notional amount. Since we're looking at a one-year maturity floor on the one-year interest rate with a strike of 8%, we need to calculate the value of this floor given the current one-year zero-coupon rate of 6%.The formula to calculate the price of a floor is not directly provided, but we can infer that the floor is out of the money (since the strike rate of 8% is higher than the current one-year rate of 6%), and thus, its value will depend on the probability of the one-year rate falling below the strike rate in the future. However, given the information provided and the nature of the question, it seems we are expected to calculate the price of the floor using a simplified approach or a direct calculation.Given the lack of specific formula or method for calculating the floor's value in the question, and considering the BDT model's complexity, we can't directly compute the exact price without more information (like the risk-neutral probabilities of interest rate movements). However, the correct answer is provided as an option, suggesting that there might be a straightforward calculation or an assumption I'm missing in this explanation.In the context of the BDT model and given the information, the correct answer would typically involve calculating the expected payoff of the floor based on the probability of the interest rate falling below the strike rate and discounting that payoff back to the present value using the appropriate discount rate. Without the explicit formula or method to calculate this in the question, we rely on the provided options to guide the response.

Assume Annual Compounding σ=0.30\sigma = 0.30σ=0.30 What Is the Price of a One-Year Maturity Floor

Assume Annual Compounding $\sigma = 0.30$ What Is the Price of a One-Year Maturity Floor