Consider a Stop-loss option with value function V(S, J) in the case where thereare continuous dividends paid at rate D. A similarity reduction of the formW(n) =V/J with n = S/J leads to¹o²³n²W" + (r = D)nW' − rW = 0,which must be solved subject to-W (1) W'(1)=0 and W(A) = X.-The current value of the underlying is S = 1. What is the current value ofthe Stop-loss option assuming What is the value of a Stop-loss option withr = 0.25, σ = 0.4, D = 0.2 and λ = 0.9. Present your results to a minimum of4 decimal places.

# Understanding the Stop-Loss Option Valuation## Introduction to Stop-Loss OptionsA stop-loss option…

Answered: Consider a Stop-loss option with value…

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter15: Decision Analysis

Section: Chapter Questions

Problem 6P

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Suppose the demand functions for two products are q1 = f(p1, p2) and q2 = g(p1, p2) wherep1, p2, q1, and q2 are the prices (in dollars) and quantities for products 1 and 2. Consider thefour partial derivatives∂q1/∂p1,∂q1/∂p2,∂q2/∂p1and ∂q2/∂p2,State the sign of each of these partial derivatives if:(a) the products are complementary goods(b) the products are substitute goods.
Consider an asset S with price function S = 2+2t S(t) = S=8-t for tЄ [0,2], for tЄ [2,4], St² 8t+20 for tЄ [4,6]. (a) Sketch the graph of S(t). - (b) Calculate the continuous arithmetic average of S over the interval 0 ≤ t ≤ 6. (c) Calculate the discrete arithmetic and discrete geometric average of S, where the discrete sampling points are take at times t = t; = ist for i = 0, 1, 2,...6 with St = 1. (d) What is the payoff of a European-style discrete geometric average rate call option which expires at t = T = 6 with E = 4.2? (e) What is the payoff of a European-style continuous arithmetic average strike put which expires at t = T = 6? (f) Consider a stop-loss option with λ = 5/6. At what time will this option be exercised? What will be the payoff?
The Black-Scholes equation for the value of an option V(S,t), where S is the value of the underlying asset and t is time, can be transformed into the diffusion equation for a new variable u(x,7) using S = Ee™, t = T − 27/0², k = 2r/o² and - (k-1) x (k+1)² + T V=Eu(x,T) exp 2 4 where r is the risk-free interest rate, σ is the volatility, E is the strike price, and T is the expiry date. The diffusion equation has the solution u(x,T): = 1 TT or L 2√Tπ 1 uo (s) exp 4T : (x - s)²) ds. Determine, showing all steps, the function uo(s) for a European asset- or-nothing call with the pay-off A(S) = SH(S – E). -
* Sketch the pay-off diagram for the straddle option: A(S) = max(S- E, 0) + max(E – S, 0). -
Internal Rate of Return is the discount rate that sets NPV to 0. True or false?
Consider two different forward contracts on the same consumption asset. There are no storage costs. Today it is t = 0. One contract has maturity date T and the other has maturity date T_2 where T_2 > T_1. The risk free rate is r. Show that no arbritrage implies that:F_2 <= F_1(1 + r)^(T_2 - T_1)
State the decision criteria for each of the following. (2) PI > MIRR > NPV > IRR > options; 0 1 PI MIRR NPV IRR Payback
Hydro Ottawa has two options for upgrading a natural gas power station to meet new government standards. Option 1: Hydro Ottawa will make the upgrades themselves. This is expected to cost $12,700 at the end of each month for 12 years. At the end of the operation (in 12 years) Hydro Ottawa expects to sell all equipment needed for the upgrade for $122,000. Option 2: Pay experienced contractors. This will cost $28,000 up front and $13,900 monthly (at the end of every month) for 15 years. Assume all interest is 3.72% compounded monthly. Round the answers to NPV (Option 1), and NPV (Option 2) to the nearest dollar. Round all other answers to two decimal places where applicable. 1) Find the net present value of option 1: P/Y = C/Y = N = I/Y = PV = PMT= FV = Payments (Cost) GA % Sale of equipment (Residual) GA GA LA %
Consider a Russian option with value function V(S, J) in the case where there are continuous dividends paid on the underlying asset S at rate D. Define the variable J for this option. A similarity reduction of the form W(n) = V/J with n S/J leads to 110²² W +(r− D)nW' rW = 0, which must be solved subject to - W(1) W'(1) = 0, W(no) = 1, W'(no) = 0, where n = ŋo is the optimal exercise boundary in similarity coordinates. The current value of the underlying is S = 3. What is the current value of the Russian option assuming that σ = 0.3, r = 0.1 and D = 0.05? Present your results to a minimum of 4 decimal places.
The NPV profile: O A. shows the payback period the point at which NPV is positive. O B. shows the internal rate of return the point at which NPV is zero. OC. shows the NPV over a range of discount rates. O D. B and C are correct.
There is one period. Assume a representative agent with utility function U(ct) = αc_t − βc^2_tassume the following: α = 100, β = 1, and δ = 0.97. Consumption at t = 0 is C0 = 24. At t = 1 one of two states θ1 and θ2 eventuate with probability π1 = 0.5, and π2 = 0.5,respectively. There are two complex securities s^1 and s^2.s^1 has a payoff of 23 in θ1 and 27 in θ2.s^2 has a payoff of 20 in θ1 and 32 in θ2.What is the stochastic discount factor mt+1? hint: Recall mt+1 =δU′(ct+1)/U′(ct)
Derive the Karush-Kuhn-Tucker conditions for this Bid-price policy program (also shown in the image for clarity),min J˜µT(x)s.t. µ ≥ 0with variable µ ∈ ℝ^m. In particular, show that an optimal solution µ* to this program must satisfy the constraints in the image below:

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