A stock is by and by selling at a cost ot $50 per catch. Atter one time span, its selling cost will

(in present worth dollars) be either $150 or S25_ A choice to buy y units ot the stock at tme

1 can be bought at cost cy.

(a) What should c be all together peak there to be no certain success?

(b) It c = 4, clarify now you could ensure a definite success.

(c) It c = 10, clarify now you could ensure a definite success.

(d) utilize the exchange hypothesis to verity your response to section (a).

question 34

The current cost ot a stock is 100. Assume that the logarithm ottne cost of the stock changes

as per a Brownian movement measure witn float coefficient u = 2 and fluctuation boundary 02

1. Give the BlackScholes cost ot an alternative to purchase the stock at time 10 peak an expense ot

(a) 100 for each unit

(b) 120 for each unit

(c) 80 for every unit

Expect that the consistently accumulated loan fee is 5%

A stochastic interaction is supposed to be a Martingale cycle {Y(t), t 2 0} if, pinnacle s <

qustion 35

Show that {Y(t), t 2 0} is a Martingale when

Y(t) exp{c8(t) c2 t/2}

where c is a subjective consistent. What is ?

A significant property ot a Martingale is that it you ceaselessly notice the cycle and afterward stop

eventually T, at that point, subject to some specialized conditions (which Will hold in the issues to be

thought of),

The time T as a rule relies upon the upsides of the cycle and is known as a halting tjme pinnacle the

Martingale. This outcome, that the normal worth ottne halted Martingale IS equivalent to its fixed tme

assumption, is known as the Martingale halting hypothesis.

question a day and a half

Let {X(t), t 2 0} be Brownian movement witn float coefficient u and change boundary 02. That is,

X(t) 08(t) + ut

Let > O, and pinnacle a positive steady x let

T - Ming: X(t) = x)

= Min t: B(t)=

That is, T is the first run through the interaction {X(t), t 2 0) hits x. utilize the Martingale halting hypothesis to

snow that