15-MATH-941 Seminar
in Financial Mathematics
Optimal Portfolios, Risk Premium,
Interest Rates, Quantitative Equity, and Foreign Exchange
– Wednesday nights
6:00-8:40 PM
This course is intended for
advanced MS and PhD students as well as the continuing education for the
professionals in quantitative finance. It was developed over a number of years
of executive training under the auspices of GARP (http://www.garp.com),
RISK Training (http://www.incisive-events.com/),
and in-house financial industry training/consulting.
Optimal portfolio theory for general multi-factor
Markovian Ito-SDE markets
- Multi-factor, multi-tradable, complete and
incomplete, Markovian Ito-SDE markets
- Optimal portfolio problems, without or with
constraints on the portfolio
- HJB PDE, Monge-Ampere type PDE, mildly non-linear
(risk-premium) PDE characterizations of the value function
- An explicit solution example: optimal portfolio
under stochastic market appreciation rate
- Major ramifications of the modern optimal
portfolio theory:
1.
better portfolio
management
2.
better pricing
theory: mathematical determination of the pricing risk premium
3.
better hedging,
risk management
4.
better FX rate
theory
Risk premium, derivative Pricing and Hedging in
incomplete markets
- Pricing of multi-contracts in multi-factor,
multi-tradable, complete and incomplete, Markovian Ito-SDE markets using
HARA and CARA utilities of wealth
- The most general Black-Scholes type pricing PDE
(system) with risk premium determination
- General hedging formula (for complete and
incomplete markets)
- An Explicit solution example: pricing variance
swaps with risk premium determination (how does the general market
sentiment affect the price of variance swaps?)
Extensions to American options
- Risk premium for American options – does it
differ from the one for European options?
- Fast sparse array Mathematica algorithm for
solving the one-space-dimension finite difference free boundary problem
for pricing of American contracts
Interest Rates
- Short rate models for stochastic interest rates
- Incomplete market bond pricing using HARA utility
of wealth (and the impossibility of CARA pricing under stochastic interest
rates)
- Historical US yield curve fitting: could the risk
aversion explain/quantify the humped yield curve?
Quantitative Equity
- Classical Miller-Modigliani theory of firm value
– Black’s dividend puzzle
- When does the dividend policy affect the total
investors gain and when it does not?
- Firm value and its volatility via incomplete
market pricing theory
- An explicit valuation formula under stochastic
revenue and cost rates
- An explicit valuation formula under dynamic
market share
FX rates and FX derivatives
- The optimal-portfolio based, general diffusion
theory of FX rates
- why JPY falls when investors ignore risks –
understanding and quantifying
- The effect of market volatility on FX rates
- FX rates under stochastic interest rates
- FX rates under stochastic volatility
- The general diffusion model for FX derivatives –
the general risk premium PDE and the general pricing PDE
- FX derivatives under stochastic interest rates
- FX derivatives under stochastic volatility
- The most conservative hedging in complete and
incomplete FX markets
Implementation, statistics and further empirical
verification
- Pricing and hedging of FX futures, FX options,
and other derivatives, with correct risk premium
- Explicit solutions
- Fourier Transform solutions
- Statistical estimation of model parameters
- Implied volatility skew
- The effect of market risk aversion on the price
of FX derivatives
- Hedging implementation and assessment of
hedging-efficacy
For more information please contact
Prof. Stojanovic at Srdjan@math.uc.edu
or 513-556-4064.