Volatility risk has played a major role in several financial debacles (for example, Barings Bank, Long Term Capital Management). This risk could have been managed using options on volatility which were proposed in the past but were never offered for trading mainly due to the lack of a tradable...

This paper is a theoretical examination of the stochastic behavior of equilibrium asset prices in an economy consisting of a production process controlled by a state variable representing the state of technology. The investors with different degrees of risk aversion and time preferences trade...

Using no arbitrage principle, we derive a relationship between the drift term of risk-neutral dynamics for instantaneous variance and the term structure of forward variance curve. We show that the forward variance curve can be derived from options market. Based on the variance term structure, we...

VIX futures are exchange-traded contracts on a future volatility index level (VIX) derived from a basket of SPX stock index options. The paper posits a stochastic variance model of VIX time evolution, and develops an expression for VIX futures. Free parameters are estimated from market data over...

This paper studies the pricing and hedging of continuously sampled arithmetic average rate options. We derive a new analytical approximate formula to price and hedge the arithmetic average rate options. The correction to the analytical approximate formula is governed by a Partial Differential...

This paper analyzes and values European-style options on the minimum or the maximum of two average prices. In particular, we provide a closed-form pricing formula for the option with geometric averaging starting at any time before maturity. Our numerical evidence shows that the use of the...

This paper studies the pricing of Arithmetic Asian options with continuous sampling. We derive a new analytical approximate formula to price and hedge the Arithmetic Asian options. The correction to the analytical approximate formula can beevaluated by solving a Partial Differential Equation...

Volatility risk has played a major role in several financial debacles (for example, Barings Bank, Long Term Capital Management). This risk could have been managed using options on volatility which were proposed in the past but were never offered for trading mainly due to the lack of a tradable...

Volatility risk has played a major role in several financial debacles (for example,Barings Bank, Long Term Capital Management). This risk could have been managed using options on volatility which were proposed in the past but were never offered for trading mainly due to the lack of a tradable...

This paper analyses the new market for trading volatility; VIX futures. We first use market data to establish the relationship between VIX futures prices and the index itself. We observe that VIX futures and VIX are highly correlated; the term structure of VIX futures price is upward sloping while...