Fall 2019
project 案例project You may choose any of these projects. Two people per project. The output is analysis (Excel or Jupyter Notebook)
You may choose any of these projects. Two people per project. The output is analysis (Excel or Jupyter Notebook), together with a Word or other PDF writeup. The project first draft is due on Dec 11-12, according to your class day.
Project 1
Using the mixture of lognormals method, develop a spreadsheet or Python tool to (a) estimate the parameters from market S&P option prices (b) plot the implied risk-neutral distributions from market option prices and (c) plot the implied volatilities of the model. Write up one example in detail for your boss, which explains your methodology and results using a specific set of option prices, perhaps a sequence in calendar time for the same maturity, or a snapshot of different maturities at a point in time. Don’t worry about overfitting, the object is to get an accurately shaped distribution within the mixture of normals distribution class. If you are using American options, for the purpose of this exercise, we will assume they are European.
Project 2
Please see the Shout option spreadsheet tab for instructions. Basically, you will assume the role of an exotic equity derivatives analyst, price the shout option, determine the optimal exercise strategy, and provide traders instructions on how to best hedge the shout option using traded options. Finally, you will prepare a profitability and risk assessment for management. A complete day in the life of a desk quant!project代写
Project 3
J.G. Wentworth (JGW) purchases structured settlements from individuals. Structured settlements are promises insurance companies have made to pay individuals in the form of annuities over time. For example, if someone has a disabling accident, the insurance company may pay $10,000 per month to the accident victim as a result of a court judgment or a settlement with the insurance company. See https://www.youtube.com/watch?v=cN9OKXtzHtE for one of their commercials designed to entice customers to consider exchanging their settlements for cash now.
There are about $5.4 billion notional in settlements that have been sold to JGW, including obligations from approximately 250 different insurance companies or obligors, lasting up to 60 years. We will assume $5.4 billion from 50 obligors, with payments lasting 10 years for the purposes of our analysis. You may assume annual payments, and assume that the cash flows are equal in all years and for all obligors. You may also assume that JGW purchases the structured settlements at a pretax discount rate of 10% per year based on the promised payments.project
However, not all promised payments from obligors are received.
Insurance companies rarely default on their claims, because the payments are guaranteed in the U.S. by state funds designed to protect insurance policyholders. However, when an insurance company is placed into receivership, i.e. controlled by the regulators due to financial troubles, sometimes the structured settlement beneficiaries are offered a discounted payout to avoid the cost and delay of recovering the payments that have been promised to them.
A.M. Best (AMB) is a rating agency that specializes in insurance companies. AMB provides historical impairment rates for insurance companies. We will use the 1-year impairment rates as a proxy for the probability of default per year and therefore subsequent loss. In the event of loss, the discount or loss given default will be assumed to be 30%. Once a default occurs, all future payments from that obligor are reduced by 30%. You may assume that of the 50 insurance company obligors, 10 of them have A++ ratings from AMB, 10 A+, 10 A, 10 A- and 10 B++. You may assume their default dates are independent random variables. Set up your spreadsheet so you can change the ratings distribution, and include all rating categories from the AMB table on the next page.
Valuation Exercise project
We assume the equity investors require a pretax return of 6% p.a., and the risk-free pretax discount rate is 2% p.a. Build a spreadsheet to simulate the losses using 1000 simulations of fixed random numbers, and find the present value of the expected cash flows at the risk-free rate. Begin by assuming that the portfolio of claims is funded by equity, i.e. JGW raised equity capital and used it to finance the purchase of the receivables. We ignore costs and any other liabilities. Show the value of equity, the expected distribution of equity present values, and the expected dividend flows, assuming all cash flows are paid out as dividends. The question we will ask over time is how we can improve JGW’s balance sheet, specifically the value of its equity.
Financing exercise
JGW has two options available for financing. One is a fixed-rate fully amortizing 10-year financing program offered at a 4% pretax yield, with annual debt payments limited to 65% of the promised payments. Debt must be paid off before dividends are paid, and there is no prepayment penalty. The corporate tax rate is 35%.
The second option is a collateralized loan obligation, or CLO. In this structure, different lenders can choose their risk profiles. “Senior” noteholders, or Class A noteholders, have their interest and principal paid before “junior” Class B noteholders. The issuer, JGW keeps the cash flows after A and B have been paid. We will assume a highly simplified waterfall structure:
Class A has a stated pretax yield of 3% based on 60% of promised payments. Class B has a stated pretax rate of 5% based on an additional 35% of promised payments. Any residual cash flows accrue to the issuer.
Use your simulator to value the two financing options. Show the balance sheets and the expected cash flow trajectories of all the security holders, equity, debt, or CLO. Which debt would you most like to own?
Risk management exercise
JGW can purchase a wrapper, an insurance policy on its portfolio that will make the company whole on any defaults. What is the maximum value of the wrapper, expressed in basis points per year? How does your answer vary with the credit rating of the insurance company, assuming the same default logic for the wrapper as for the obligor payments?
Strategy project
Finally, assuming that JGW has more sales every year, what business strategy would you suggest to maximize long-term equity value?
Project 4
The Value of Waiting to Invest Author(s): Robert McDonald and Daniel Siegel Source: The Quarterly Journal of Economics, Vol. 101, No. 4 (Nov., 1986), pp. 707-728 Published by: Oxford University Press Stable URL: http://www.jstor.org/stable/1884175
Robert McDonald and Daniel Siegel wrote a paper, published in 1986, that argues that the present value of an investment should consider not only the current PV of benefits and the PV of costs, but also the value of waiting to make the investment at a later date. If making the investment is irreversible, but the decision to defer is reversible, this asymmetry creates value for companies deciding when to make investments.project代写
We assume that the expected monthly cash flows of an investment follow a Geometric random walk, as does the cost of investment. These may be correlated. The investment may be made any month, but once made, is not reversible.
Build a spreadsheet simulator with a revised net present value rule that considers the value of waiting to invest, and to determine a rule for deciding at any given time if it is optimal to invest.
Using illustrative parameter values, show your rules graphically, and show the value of the waiting option.
Project 5
Design your own valuation project. The project must demonstrate the use of simulation, optimization and benchmarking techniques, and must use actual market pricing data. Be sure to provide the Excel spreadsheet or Jupyter Notebook showing your valuation results. Also discuss the optimal hedging strategy using futures and/or options, and the risk assessment for the hedged position. As an example, you might consider investigating the GMDB (Guaranteed Minimum Death Benefit), which is a kind of lookback option that insurance companies offer to investors in Variable Annuities.
