응용수학 세미나
연사 : 최정민박사 (Florida State University)
제목 : Partial Hedging in financial markets with a large agent
일시 : 2008.5.14 (수) 오후 4:30
장소 : 산업경영학동 3층 세미나실 3321호
내용 : We investigate the partial hedging problem in financial markets
with a large agent. An agent is said to be large if his/her trades
influence the equilibrium price. We develop a stochastic
differential equation with a single large agent parameter to model
such a market. We focus on minimizing the expected value of the
size of the shortfall in the market with a large agent. A Bellman
type partial differential equation is derived for the shortfall
function, and the Legendre transform is used to consider the dual
shortfall function. An asymptotic analysis leads us to conclude
that the shortfall function (expected loss) increases when there
is a large agent, which means that one would need more capital to
hedge away risk in the market with a large agent. This asymptotic
analysis is confirmed by performing Monte Carlo simulations.
Finally we estimate the large agent parameter using historical
option price data from CBOE (Chicago Board Options Exchange). The
parameter is positive but small, indicating presence of the large
agent effect and justifying the validity of the asymptotic
analysis.
강연 주제 : 금융수학