Question: 2. Let 0 < K < K2. In the Black-Scholes market, consider the contingent claim X that pays one unit of the currency, provided

2. Let 0 < K < K2. In the Black-Scholes market, consider

2. Let 0 < K < K2. In the Black-Scholes market, consider the contingent claim X that pays one unit of the currency, provided S(T), the price of a share of stock at the maturity time T, belongs to the interval [K1, K2). For te [0, T), find the fair price II(t) of the claim X. Write down II(t) by using the function N(d). Hint. Denote by XIK1.Ka)(x) the indicator function of the interval [K1, K2), i.e., X[K1,K2) (x) : S1, if z E (K1, K2), 0, otherwise. %3D Use that X = X[K1,Ka (S1(T)), and note that dy Le- dy = N(b) N(a). V27 1 dy : %3D %3D 27 27 Recall that N (d) denotes the distribution function of the standard normal distribution, 1 N(d) = dy.

Step by Step Solution

★★★★★

3.38 Rating (148 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Step by step solution 1A x el ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Explain the factors used in the Black Scholes option valuation model. What is the relationship between each factor and the value of the option?

What is the current price of a share of stock for a firm with $5 million in balance-sheet equity, 500,000 shares of stock outstanding, and a price/book value ratio of 4?

Let z denote a variable that has a standard normal distribution. Determine each of the following probabilities: b. P 2.36) d. P1.14z 3.35) aPiz

Suppose that a particle starts at the origin of the real line and moves along the line in jumps of one unit. For each jump, the probability is p (0 p 1) that the particle will jump one unit to the...

a) Bachelier (1900) model. Solve the stochastic differential equation \[ \begin{equation*} d S_{t}=\alpha S_{t} d t+\sigma d B_{t} \tag{6.41} \end{equation*} \] in terms of \(\alpha, \sigma \in...

The paper The Truth About Lying in Online Dating Profiles (Proceedings, Computer-Human Interactions [2007]: 14) describes an investigation in which 40 men and 40 women with online dating profiles...

Consider the M/G/1 model with = 0.2 and = 0.25. T (a) Use the Excel template for this model (or hand calculations) to find the main measures of performanceL, Lq, W, Wqfor each of the following...

Let X 1 , . . . , X n be i.i.d. random variables with mean and variance 2 . Let x = (X 1 + + X n )/n be the average. (a) Find E[x|X 1 ]. (b) Find V[ x |X 1 ].

Figure 8(B) shows a slice of ham on a piece of bread. Prove that it is possible to slice this open-faced sandwich so that each part has equal amounts of ham and bread. By Exercise 36, for all 0 ...

Assume the Black-Scholes framework. For t 0, let S(t) be the time-t price of a stock. Consider a 9-month European contingent claim on the stock. You are given: (i) The stocks volatility is 35%. (ii)...

Accruals Current assets Interest expense Sales revenue A firm in the third year of depreciating its only asset, which originally cost $173,000 and has a 5-year MACRS recovery period $15.400 116,000...

Suppose that the random variable X has a lognormal distribution with parameter values = -0.3 and = 1.1. Find: (a) E(X) (b) Var(X) (c) The upper quartile of X (d) The lower quartile of X (e) The...

Find the volume using the washer method of the solid generated by revolving the region in the second quadrant; bounded above by the curve y = - x 3 , below by; he x - axis, and on the left by the...

Three beans are selected from a large jar containing equal amounts of white beans and red beans. An outcome is represented by a string of the sort RWW (meaning the first bean is red, the second is...

A DJ is going to pick 5 songs for a playlist. She will choose from 13 songs, 6 of which are country songs and 7 of which are rock songs. (If necessary, consult a list of formulas.) (a) In how many...

Problem #1: Consider steady state flow of an incompressible Newtonian fluid between two concentric cylinders of a rheometer as shown in Figure 1. The inner cylinder of radius R1 is rotating at a...

4. Explain with circuit and plots for the voltage and current relations in R, L, and C circuits separately? Explain resonance in electrical circuit? Calculate the capacitive reactance (X.) and...

What five functions do American political parties perform?

Where an officer encounters a vehicle pulled over to the side of a road, has no suspicion of illegal activity, and administers field sobriety tests, this action may be upheld on the community...

2. Let Fp(n, k) denote the number of permutations of {1,...,n} having exactly k fixed points, for n > 0 and k > 0. Fp(0,0) is 1 (there is exactly one permutation of the empty set, and it doesn't have...

1. Let D be 2. Let G = {a + b D : a, b Q} \ {0}. Define multiplication by (a + b D)(c + d D) = (ac bdD) + (ad + bc) D. Show that G is a group with respect to multiplication. 2. Let r be 5 Let H = { x...

Double-exponential distribution. Let X1, , Xn be a sample from the double-exponential distribution with density 1 2 e|x| . The LMP test for testing 0 against > 0 is the sign test, provided the...

void countingSort(int A[1...n], int k) 1: //Precondition: The n values in A are all between 0 and k 2: Let C[0... k] be a new array 3: //We will store our sorted array in the array B. 4: Let B[1...n]...

Question 1. Let K be an algebraically closed field. (1) Consider the polynomial map F : K2 - K, (X, Y) > Y. Show that the image F(V) of the affine variety V = V(XY - 1) is open. (2) Let F : K" -> Km...

Let D be 2. Let G = {a + bD : a, b Q} \ {0}.Define multiplication by (a + bD)(c + dD) = (ac bdD) + (ad + bc)D. Show that G is a group with respect to multiplication. 2. Let r be 5 Let H = {x yy x +...