[l] [a] The payoﬂ' @[S] is as in the picture below.
[b] The payoﬂ' is @(S) = [80 — S]+ + [S — 120]+, Le. a sum ofa put and a all.
(c) When 34 = 0, we will have .‘3n = 0 for t <_I u <_: T. Exercising the option at time u will then
yield 80, which mrrespond
{1} Suppose I wish to compute the value of a European Stmddte option on a stock. The option pays (11(5) if
exercised when the stock price is S, where
52—5 ifS<52
if; = _
{1' {3—52 H.925?
The current value of the stock is 53 and it. expires 9 months from t
[l] [a] The exaet selutien is 11(1) = 5-32}?
(h) The diseretizatien is
un|l_2un 1 un—l un|l_un
,5, =
(&I]2 n I :1: i n
seweget
_ 2| n-l A31 |
Ii"lﬂll— l|nAz' “_l|niAz'zu“—l
1.10: l
1.11:1
[e] The diseretizatien is
i-I|-a-L|l—2'1I|Ir|i'f-Il-ri—l un—un—l
—
Question 1
la} T= 0.5, F 0.031 D=CILOL Sigma=0.2, SD=T5
European Strangle option = Euro Call option [K=120) + Euro Put option (K=30}
Apply BS formula; we obtain (For continuous paying dividend stock, basically,
just replace So with Sne'm]
Euro Strangle pr
{1) Suppose I wish to compute the value of a European put option on a stock with strike price 23. The
current. value of the stock is 29 and it expires 9 months from today. The stock volatility is a = ".18 and
the risk free interest rate is r- = 0.04. The