We reconsider the problem of the optimal time to sell a stock studied by Shiryaev et al. (2008) (following in this issue of Quantitative Finance) using path integral methods. These methods allow us to confirm the results obtained by these authors and extend them to the entire parameter region....

This paper contains a statistical description of the whole U.S. forward rate curve (FRC), based on data from the period 1990-1996. We find that the average deviation of the FRC from the spot rate grows as the square- root of the maturity, with a proportionality constant which is comparable to...

Financial time series exhibit two different type of non-linear correlations: (i) volatility autocorrelations that have a very long-range memory, on the order of years, and (ii) asymmetric return-volatility (or 'leverage') correlations that are much shorter ranged. Different stochastic volatility...

We decompose, within an ARCH framework, the daily volatility of stocks into overnight and intra-day contributions. We find, as perhaps expected, that the overnight and intra-day returns behave completely differently. For example, while past intra-day returns affect equally the future intra-day...

We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily returns. The standard ARCH or GARCH framework is recovered...

We discuss two more universal features of stock markets: the so-called leverage effect (a negative correlation between past returns and future volatility), and the increased downside correlations. For individual stocks, the leverage correlation can be rationalized in terms of a new...

We define and study a market model, where agents have different strategies among which they can choose, according to their relative profitability, with the possibility of not participating to the market. The price is updated according to the excess demand, and the wealth of the agents is...

We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between ‘active’ and ‘inactive’ strategies is subordinated to random-walk like processes. We numerically...

We propose a new ‘hedged’ Monte-Carlo (HMC) method to price financial derivatives, which allows to determine simultaneously the optimal hedge. The inclusion of the optimal hedging strategy allows one to reduce the financial risk associated with option trading, and for the very same reason...

We consider the problem of the optimal trading strategy in the presence of linear costs, and with a strict cap on the allowed position in the market. Using Bellman's backward recursion method, we show that the optimal strategy is to switch between the maximum allowed long position and the...