Question

Assume that a $75 strike call has a 1.0% continuous dividend, 90 days until expiration and stock price of $72.00. What is the rho of the option as the interest rate changes from 6.0% to 5.0%? Assume sigma=0.27

A) 0.07 B) 0.12 C) 0.16 D) 0.20

Want to know the steps with formulas please.
The ans is A.

Answer 1

Where,

S₀ = underlying price ($$$ per share)

X = strike price ($$$ per share)

? = volatility (% p.a.)

r = continuously compounded risk-free interest rate (% p.a.)

q = continuously compounded dividend yield (% p.a.)

t = time to expiration (% of year)

d₁ = {-0.0408 + 0.2466 x ( 5% - 1% + [0.27²2])} 0.27 x 0.4966 = - 0.0219 0.1341 = - 0.1633

d₂ = - 0.1633 - 0.1341 = - 0.2974

N(d₂) is area to the left of Z value in the cumulative Z table. Since, only positive values are given, to find N(- 0.29) we find area to the left of 0.29 and subtract it from 1. [1 - 0.6141 = 0.3859]

N(d₂) = 0.3859

Rho = (75 x 0.2466 x 0.9877 x 0.3859) 100 = 0.070

Option A is correct.