財務工程簡介課程大綱
Unit 1: Introduction to
Financial Engineering
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The Definition of Financial
Engineering
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The Environment of Financial
Engineering
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The Evolution of Derivatives
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Financial Engineering
and Risk Management
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The Case of Financial
Engineering in Taiwan
Unit 2: Equivalent Martingale Measures and Risk-Neutral
Pricing
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Risk-Neutral Pricing: A Binomial Example
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An Economic Interpretation of Risk-Neutral Probabilities
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Arbitrage and Non-Existence of Risk-Neutral Probabilities
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Risk-Neutral Probabilities and Completness
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A Black-Scholes Example
Unit 3: Alternative Option Pricing Models
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Option Pricing Models Under Stochastic Interest Rates
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Option Pricing Models Under Stochastic Volatility
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Option Pricing Models Under Jump
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Option Pricing Models With Transaction Costs
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Applications
Unit 4: Term Structure Models of Interest Rates
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Introduction
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Issues of the Term Structure Model
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Vasicek (1977) Model
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Cox, Ingersoll and Ross (1985) Model
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Multi-Factors Models
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Ho and Lee (1986) Model
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Heath, Jarrow, and Morton (1990, 1992) Model
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Hull and White (1990) Model
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Black, Derman and Toy (1990) Model
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Empirical Issues
Unit 5: Interest Rate Derivatives
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Bond Options
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Caps and Floors
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Interest Rate Swaps
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Swaptions
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Differential Swaps
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Equity Swaps
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Convertible Bonds
Unit 6: Exotic Options
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Classifications:
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Path dependent vs path independent
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Early exercise problem
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Single variable vs. Multiple Variables
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Asian Options
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Lookback/Binary/Barrier Options
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Rainbow Options
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Bermudan Options
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Pricing Issues
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Hedge Issues
Asian Options: An option with a payoff dependent on
the average price of the underlying asset
during a specified period.
Barrier Options: An option whose payoff depends on
whether the path of the underlying asset
has reached a barrier (i.e., a certain predetermined level).
Binary Options: Either a cash-or-nothing option or
an asset-or-nothing option.
Black-Scholes Model: A model for pricing European
options on stocks, published by
Fischer Black and Myron Scholes in 1973.
Bond Options: An option in which a bond is the underlying
assets.
(Interest Rate) Caps (Floors) : An option that provides
a payoff when a specified interest rate
is above (below) a certain level.
Convertible Bonds: Corporate bond that can be converted
into a predetermined amount of
the company's equity at certain times during its life.
Derivative: Instrument whose price depends on or is
derived from the price of another asset.
Differential Swaps: Swap in which a floating rate
in one currency is exchanged for
a floating rate in another currency, with both rates being applied to
the same principal.
Equity Swaps: Swap in which return on an equity portfolio
is exchanged for either a fixed or
a floating rate of interest.
Hedge: A trade designed to reduce risk.
Interest Rate Swaps: An exchange of a fixed rate of
interest on a certain notional principal
from floating rate of interest on the same notional principal.
Lookback Options: Option whose payoff depends on the
maximum or minimum of
the asset price achieved during a certain period.
Option: The right to buy or sell an asset.
Swaptions: Option to enter into an interest-rate swap
in which a specified fixed rate is
exchanged for a floating rate.
Term Structure: Curve relating interest rates to maturity.
Transaction Cost: Cost of carrying out a trade. (Equal
to commissions plus the difference
between the price obtained and the midpoint of the bid-offer spread.)
Volatility: Measure of the uncertainty of the return
realized on an asset.
Vasicek, O.A. (1977). An Equilibrium Characterization
of the Term Structure,
J. of Financial
Economics 5 177-188.
Cox, J.C., J.E. Ingersoll, and Ross, S.A. (!985) A
Theory of the Term Structure of Interest Rates,
Econometrica 53 385-407.
Ho, T.S.Y. and Lee, S.B. (1986) Term Structure Movements
and Pricing Interest Rate Contingent
Claims, J. of Finance 41 1011-1029.
Heath, D., Jarrow, R. and Morton, A (1990) Bond Pricing and
the Term Structure of Interest Rates:
A Discrete Time Approximation, Journal of Financial and
Quantitative Analysis 25 419-440.
Heath, D., Jarrow, R. and Morton, A (1992) Bond Pricing and
the Term Structure of the Interest Rates:
A New Methodology, Econometrica 60 77-105.
Hull, J.C. and White, A. (1990) Pricing Interest Rate
Derivative Securities,
Review of Financial
Studies 3 573-592.
Black,F., Derman, E. and Toy, W. (1990) A One-Factor Model
of Interest Rates and Its Application
to Treasury Bond Options, Financial Analysts Journal
33-39.
Created: March 5th, 2000
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Back to the home page of Hung Chen.
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Connect to the home page of Department
of Mathematics, National Taiwan University, Taiwan.
hchen@math.ntu.edu.tw