Financial Engineering

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Financial Engineering

• Tyler Yang
• for
• Asian Real Estate Society
• July 4, 2002

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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 investors objectives

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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

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Types of Cash Flows
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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)

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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

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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

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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

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Equilibrium (Risk-adjusted Return) Approach

• CAPM
• APT/Multi-factor CAPM

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Cash Flow Projection

• Actuarial based distribution of outcomes

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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

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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

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Risk-Neutral Probability
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Risk-Neutral Approach

• Risk-adjusted probability
• Pseudo probabilities
• Discount risk-adjusted expected cash flows at
  risk-free rate

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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

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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

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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

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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

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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

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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

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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

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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 investors objectives and
  constraints
• To hedge or not to hedge?
• Value-at-Risk applications
• Capital adequacy requirements for regulator,
  rating agency, stock holders

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Example Striping MBS
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Expand Research Scope

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