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Financial Engineering

Financial Engineering. Tyler Yang for Asian Real Estate Society July 4, 2002. Financial Engineering. Trading Perspective Create structured securities from basic assets to catch specific market niches Modeling Perspective

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Financial Engineering

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  1. Financial Engineering Tyler Yang for Asian Real Estate Society July 4, 2002

  2. Financial Engineering • Trading Perspective • Create structured securities from basic assets to catch specific market niches • Modeling Perspective • Develop/apply contingent claim valuation methods to price exotic structured securities • Management Perspective • Assess the uncertainty of future payoff of portfolio • Determine strategies to restructure the portfolio risk-return to meet investor’s objectives

  3. Trading Perspective • Design structured security to satisfy market demand • Examples: • Futures Option, Swaption, Spread Option • Convertible bond, Callable bond, Index bond, Floater • CMO, IO, PO • CDO, Credit swap, Credit linked bond • ABS, Lease, Real option

  4. Types of Cash Flows

  5. Cash Flow Structure • Un-guaranteed MBS • CF1 = Collected Interest + Amortized Principal + Prepaid Principal + Default Recovery • Guaranteed MBS • CF2 = CF1 + Default Principal – Default Recovery + Uncollected Interest • IO Strip (Servicing Right) • CF3 = Collected Interest (+ Uncollected Interest)

  6. Cash Flow Structure – continued • PO Strip • CF4 = Amortized Principal + Prepaid Principal + Default Recovery (or Default Principal) • Servicing Right • CF5 = Servicing Fee – Servicing Expense • Guarantee Contract • CF6 = Guarantee Fee – Default Principal + Recovery - Expense

  7. Valuation • Expected Cash Flows discounted at risk-adjusted return (assume to be 7.25%) • Value of Uninsured MBS = 99.28 = Value of IO + Value of PO • Value of Insured MBS = 100.00

  8. Modeling Perspective • Cash flow allocation • Discounted cash flows • Discount expected cash flows by a Risk-Adjusted Return • Discount risk-adjusted cash flows by risk-free

  9. Equilibrium (Risk-adjusted Return) Approach • CAPM • APT/Multi-factor CAPM

  10. Cash Flow Projection • Actuarial based distribution of outcomes

  11. Equilibrium Approach • Stock value can up to $200 with 70% probability and down to $50 with 30% probability when risk-free rate is 10% • Expected payoff = .7 (200) + .3 (50) = $155 • u = 200/100 = 2 • d = 50/100 = 0.5 • r = 1.10 • Risk-adjusted return = 155/100 - 1 = 55% • Risk premium = 55% - 10% = 45%

  12. Equilibrium Approach • A call option with exercise price = $125 • Possible payoffs are $80 with 70% probability and $0 with 30% probability • Expected payoff of option = .7 (80) + .3 (0) = $56 • Beta of the option = b(C) = 1.83 • Risk-adjusted return = k(C) = 10% + 1.83 (45%) = 92.5% • Option Value = C = 56/(1.925) = $29.09

  13. Risk-Neutral Probability

  14. Risk-Neutral Approach • Risk-adjusted probability • Pseudo probabilities • Discount risk-adjusted expected cash flows at risk-free rate

  15. Risk-Neutral Approach • Risk-neutral probability (u) = = 0.4 • Risk-neutral expected payoff of stock = .4 (200) + .6 (50) = $110 • Stock price = 110/1.10 = $100 • Risk-neutral expected payoff of the call option = .4 (80) + .6 (0) = $32 • Option value = $32/1.10 = $29.09

  16. Model Solutions • Closed form solutions • Black-Scholes model, Vasicek model • Finite Difference Methods • Implicit • Explicit (trinomial tree) • Binomial tree • Monte Carlo Simulation • Risk-neutral process • Actuarial based process

  17. Examples • Lattice Method (Binomial Tree) • American Put Option • Monte Carlo Simulation • Bond pricing under the Hull-White term structure model • Value-at-Risk by Bootstrapping

  18. Closed Form Solutions • Pros • Fast • Easy to implement • Cons • Can only work under limited simplified assumptions, which may not satisfy trading needs • May not exist for all derivative contracts

  19. Finite Difference Methods • Pros • Intuitively simple • Fast • Capture forward looking behavior, best for American style contracts • Accuracy increases with density of time interval • Cons • Can not price path-dependent contracts • Difficult to implement, especially with time and state dependent processes

  20. Monte Carlo Simulations • Pros • Intuitive • Easy to implement • Matches VaR concept • Accuracy increases with number of simulations • Cons • Forwardly simulate cash flows, cannot handle American style contracts • Slow in convergence

  21. Combined Approaches • To handle both path-dependent and American style cash flows • Difficult to implement and time consuming • Alternative methods • Simulation through tree • Bundled simulation

  22. Management Perspective • Fundamental driving force of financial engineering • Analyze the risk and return tradeoff for different cash flow components of an asset/portfolio • Determine the optimal risk-return profile for the portfolio based on investor’s objectives and constraints • To hedge or not to hedge? • Value-at-Risk applications • Capital adequacy requirements for: regulator, rating agency, stock holders

  23. Example: Striping MBS

  24. Expand Research Scope • Mathematical and technical advancements • Volatility and hedging analysis • Financial risk management applications • Creative structure development • General equilibrium impacts • Policy implications

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