Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management)

Prerequisite Qualification 1: Probability (I) :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025

Question 1 What short-term action can be taken to improve HR value, alignment, communication, control, and coordination within the division? ❌ Hire a full staff✅ Establish regular communication❌ Install the HRIS system❌ Fully adopt corporate HR policy Explanation:In the short term, regular communication delivers immediate improvement in alignment, coordination, and control without large structural or… <a href="https://codeshala.io/platform/coursera/course/introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management/assignment/prerequisite-qualification-1-probability-i-introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management-answers-2025/" rel="bookmark">Prerequisite Qualification 1: Probability (I) :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025</a>

Introduction to Basic Fixed Income Securities :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025

Question 1 – Lottery payments (Present Value) Payment = $0.5 million per year Number of payments = 20 Interest rate = 10% annually First payment = immediate → annuity due Formula (Annuity Due): PV=PMT×1−(1+r)−nr×(1+r)PV = PMT \times \frac{1 – (1+r)^{-n}}{r} \times (1+r)PV=PMT×r1−(1+r)−n×(1+r) PV=0.5×1−(1.1)−200.10×1.1PV = 0.5 \times \frac{1 – (1.1)^{-20}}{0.10} \times 1.1PV=0.5×0.101−(1.1)−20×1.1 PV≈0.5×8.5136×1.1=4.68PV \approx 0.5 \times… <a href="https://codeshala.io/platform/coursera/course/introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management/assignment/introduction-to-basic-fixed-income-securities-introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management-answers-2025/" rel="bookmark">Introduction to Basic Fixed Income Securities :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025</a>

Introduction to Derivative Securities :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025

Question 1 – Discount rate d(0,4)d(0,4)d(0,4) Given spot rate for 4 years (annual compounding): s4=8.1%=0.081s_4 = 8.1\% = 0.081s4=8.1%=0.081 Discount factor: d(0,4)=1(1+s4)4=1(1.081)4d(0,4) = \frac{1}{(1+s_4)^4} = \frac{1}{(1.081)^4}d(0,4)=(1+s4)41=(1.081)41 (1.081)4≈1.364(1.081)^4 \approx 1.364(1.081)4≈1.364 d(0,4)≈11.364=0.733d(0,4) \approx \frac{1}{1.364} = 0.733d(0,4)≈1.3641=0.733 ✅ Answer: 0.733 Question 2 – 6-year Swap Fixed Rate Swap fixed rate ccc satisfies: c∑i=16d(0,i)=1−d(0,6)c \sum_{i=1}^{6} d(0,i) = 1 –… <a href="https://codeshala.io/platform/coursera/course/introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management/assignment/introduction-to-derivative-securities-introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management-answers-2025/" rel="bookmark">Introduction to Derivative Securities :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025</a>

Option Pricing in the Multi-Period Binomial Model :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025

Question 1 American Call Option (K = 110, T = 0.25, 15-period binomial) Using a 15-step binomial model calibrated to Black–Scholes(r=2%r=2\%r=2%, c=1%c=1\%c=1%, σ=30%\sigma=30\%σ=30%, S0=100S_0=100S0=100) withu=1.0395u = 1.0395u=1.0395, early exercise does not add value for this out-of-the-money call over a short maturity. ✅ Answer: 2.50 Question 2 American Put Option (K = 110, T = 0.25,… <a href="https://codeshala.io/platform/coursera/course/introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management/assignment/option-pricing-in-the-multi-period-binomial-model-introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management-answers-2025/" rel="bookmark">Option Pricing in the Multi-Period Binomial Model :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025</a>

Prerequisite Qualification: Probability (II), Martingale :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025

Question 1 Which statements are equivalent to X and Y being independent? (Select all that apply) ✅ For joint and marginal CDFs,FX,Y(x,y)=FX(x)FY(y)F_{X,Y}(x,y) = F_X(x)F_Y(y)FX,Y(x,y)=FX(x)FY(y) ✅ For conditional PDFs,fX∣Y(x∣y)=fX(x)f_{X|Y}(x|y) = f_X(x)fX∣Y(x∣y)=fX(x) ✅ For joint and marginal PDFs,fX,Y(x,y)=fX(x)fY(y)f_{X,Y}(x,y) = f_X(x)f_Y(y)fX,Y(x,y)=fX(x)fY(y) ✅ P[X<3,Y<1]=P[X<3]P[Y<1]P[X<3, Y<1] = P[X<3]P[Y<1]P[X<3,Y<1]=P[X<3]P[Y<1] ❌ Cov(X,Y)=0 (not sufficient)❌ Conditional independence given Z (not equivalent) Question 2… <a href="https://codeshala.io/platform/coursera/course/introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management/assignment/prerequisite-qualification-probability-ii-martingale-introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management-answers-2025/" rel="bookmark">Prerequisite Qualification: Probability (II), Martingale :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025</a>

Prerequisite Qualification: Brownian Motion, Vector :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025

Question 1 Standard Brownian motion has independent increments and martingale property. E[Xt∣Xs=1]=1E[X_t \mid X_s = 1] = 1E[Xt∣Xs=1]=1 Question 2 For Brownian motion: Xs+1=Xs+(Xs+1−Xs)X_{s+1} = X_s + (X_{s+1}-X_s)Xs+1=Xs+(Xs+1−Xs) E[Xs+12∣Xs=1]=Var⁡(Xs+1−Xs)+(E[Xs+1∣Xs=1])2=1+12E[X_{s+1}^2 \mid X_s = 1] = \operatorname{Var}(X_{s+1}-X_s) + (E[X_{s+1}\mid X_s=1])^2 = 1 + 1^2E[Xs+12∣Xs=1]=Var(Xs+1−Xs)+(E[Xs+1∣Xs=1])2=1+12 2\boxed{2}2 Question 3 X3∣X1=1∼N(1,2)X_3 \mid X_1=1 \sim N(1, 2)X3∣X1=1∼N(1,2) P(X3<2)=Φ ⁣(2−12)=Φ(0.7071)P(X_3 < 2) =… <a href="https://codeshala.io/platform/coursera/course/introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management/assignment/prerequisite-qualification-brownian-motion-vector-introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management-answers-2025/" rel="bookmark">Prerequisite Qualification: Brownian Motion, Vector :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025</a>

Prerequisite Qualification: Matrix :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025

Question 1 Correct statements: ✅ For identity matrix, we have AI=IA=AAI = IA = AAI=IA=A ❌ If C=AAC = AAC=AA, then CT=CC^T = CCT=C (not always true) ✅ For matrix transpose, (AB)T=BTAT(AB)^T = B^T A^T(AB)T=BTAT ✅ If C=ATAC = A^T AC=ATA, then CT=CC^T = CCT=C ❌ Matrix multiplication is interchangeable AB≠BAAB \neq BAAB=BA in general… <a href="https://codeshala.io/platform/coursera/course/introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management/assignment/prerequisite-qualification-matrix-introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management-answers-2025/" rel="bookmark">Prerequisite Qualification: Matrix :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025</a>

Prerequisite Qualification: Optimization :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025

Question 1 Correct statements: ❌ Alice does not need to specify short position, since long-only strategy will generate the same result as strategy allowing short positions. ✅ Alice should use the positions in each portfolio as variables. ✅ Alice should specify whether short position is allowed by constraints. Question 2 Primal: min⁡cTxs.t. Ax≥b\min c^T x… <a href="https://codeshala.io/platform/coursera/course/introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management/assignment/prerequisite-qualification-optimization-introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management-answers-2025/" rel="bookmark">Prerequisite Qualification: Optimization :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025</a>

Assignment 1 :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025

Question 1 – Forward price of silver Theoretical forward price (rounded to nearest integer): ✅ 221 Question 2 – European call option (binomial model) Option value (rounded to two decimals): ✅ 1.53 Question 3 – Minimum-variance hedging Minimum-variance hedge (number of orange juice futures contracts): ✅ 105,000 Question 4 – Risk-neutral pricing paradox Correct option:… <a href="https://codeshala.io/platform/coursera/course/introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management/assignment/assignment-1-introduction-to-financial-engineering-and-risk-management-introduction-to-financial-engineering-and-risk-management-answers-2025/" rel="bookmark">Assignment 1 :Introduction to Financial Engineering and Risk Management (Introduction to Financial Engineering and Risk Management) Answers 2025</a>