Question

Assume S = $42, K = 45, div = 0, r = 0.04, sigma(volatility)= 0.48, and 80 days until expiration. What is the premium on a knock-out put option with a down-and-out barrier of $44?

A) $2.13

B) $3.13

C) $3.47

D) $4.07

Answer: C

need details of solution

Answer 1

The down-and-out put is knocked out worthless if the asset falls to the barrier B?, while if it does not, the holder receives the payoff of a vanilla put.

This is modified version of Black schole model discussed by John C Hull , while dicussing Barrier option as below.

Calculation below

Barrier options
Using Hull								Intermediate results
Data
S	42							S*exp(-qT)	42
q	0%							K*exp(-rT)	44.6018
K	45							Sigma*sqrt(T)	0.22627
H	44							d1	-0.1525	N(d1)	0.4394	N(-d1)	0.5606
r	4%							d2	-0.3788	N(d2)	0.35243	N(-d2)	0.64757
T (80 days)	0.222222222							Lambda	0.67361
Sigma	48%							y	0.2587
								x1	-0.0532
	Call	Put						y1	0.35801
Regular options	2.736	5.338
Barrier H<K
Down-and-in	4.729	5.338
Down-and-out	-1.993	3.467