someone please help, I’m having trouble distinguishing when to 1 + r*(t/360) or 1 + r^(t/365). for the below two questions, i did the discounting completely the opposite way. could someone please clarify how to distinguish which format to use for discounting??? - bolded below
A stock is currently priced at $110 and will pay a $2 dividend in 85 days and is expected to pay a $2.20 dividend in 176 days. The no arbitrage price of a six-month (182-day) forward contract when the effective annual interest rate is 8% is closest to:
In the formulation below, the present value of the dividends is subtracted from the spot price, and then the future value of this amount at the expiration date is calculated.
(110 – 2/1.08^85/365 – 2.20/1.08^176/365) 1.08^182/365 = $110.06
Alternatively, the future value of the dividends could be subtracted from the future value of the stock price based on the risk-free rate over the contract term.
(Study Session 14, Module 37.4, LOS 37.a)
Cal Smart wrote a 90-day receiver swaption on a 1-year LIBOR-based semiannual-pay $10 million swap with an exercise rate of 3.8%. At expiration, the market rate and LIBOR yield curve are:
Fixed rate 3.763%
The payoff to the writer of the receiver swaption at expiration is closest to:
At expiration, the fixed rate is 3.763% which is below the exercise rate of 3.8%. The purchaser of the receiver swaption will exercise the option which allows them to receive a fixed rate of 3.8% from the writer of the option and pay the current rate of 3.763%.
The equivalent of two payments of (0.038 - 0.03763) × (180/360) × (10,000,000) will be made to the receiver swaption. One payment would have been received in 6 months and will be discounted back to the present at the 6-month rate. One payment would have been received in 12 months and will be discounted back to the present at the 12-month rate
The first payment, discounted to the present is (0.038 - 0.03763) × (180/360) × (10,000,000) × ( 1/1.018) = $1,817.28.
The second payment, discounted to the present is (0.038 - 0.03763) × (180/360) × (10,000,000) × ( 1/1.038) = $1,782.27
The total payoff for the writer is -$3,599.55.
(Study Session 14, Module 38.6, LOS 38.j)