Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time

We propose a novel intraday instantaneous volatility measure which utilises sequences of drawdowns and drawups non-equidistantly spaced in physical time as indicators of high-frequency activity of financial markets. The sequences are re-expressed in terms of directional-change intrinsic time which ticks only when the price curve changes the direction of its trend by a given relative value. We employ the proposed measure to uncover weekly volatility seasonality patterns of three Forex and one Bitcoin exchange rates, as well as a stock market index. We demonstrate the long memory of instantaneous volatility computed in directional-change intrinsic time. The provided volatility estimation method can be adapted as a universal multiscale risk-management tool independent of the discreteness and the type of analysed high-frequency data.

PRICING PERPETUAL TIMER OPTION UNDER THE STOCHASTIC VOLATILITY MODEL OF HULL–WHITE

The valuation of perpetual timer options under the Hull–White stochastic volatility model is discussed here. By exploring the connection between the Hull–White model and the Bessel process and using time-change techniques, the triple joint distribution for the instantaneous volatility, the cumulative reciprocal volatility and the cumulative realized variance is obtained. An explicit analytical solution for the price of perpetual timer call options is derived as a Black–Scholes–Merton-type formula.

Pricing FX Options in the Heston/CIR Jump-Diffusion Model with Log-Normal and Log-Uniform Jump Amplitudes

We examine foreign exchange options in the jump-diffusion version of the Heston stochastic volatility model for the exchange rate with log-normal jump amplitudes and the volatility model with log-uniformly distributed jump amplitudes. We assume that the domestic and foreign stochastic interest rates are governed by the CIR dynamics. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate and its volatility. The main result furnishes a semianalytical formula for the price of the foreign exchange European call option.

Traders and time: who moves the market?

Purpose – This paper is aimed to investigate the impact of different categories of traders on price and volume durations at Euronext Paris. The two series are respectively related to the instantaneous volatility and the market liquidity; hence, they are particularly suited to test microstructure hypotheses. Design/methodology/approach – A Log-autoregressive conditional duration model was adopted to include the information on the traders’ identity at the transaction level. High-frequency data were used and how the informed traders and the liquidity provider affect the arrival of market events was studied. The robustness of our results was also checked by testing different distributions and controlling for microstructure effects. Findings – It was found that informed traders and the liquidity provider exert a dominant role in accelerating the market activity. This result depends on the state of the market, i.e. it is effective only during periods of high frequency of transactions. The estimates for price durations show that a high instantaneous volatility can be mainly ascribed to a great concentration of informed traders. Informed traders are also found to shorten volume durations by clustering small-size orders to disguise their private signal. For both durations, the liquidity provider is also found to foster the market activity, likely because of his contractual duties. Originality/value – The article is of interest for researchers in the field of market microstructure, as well as for specialists in the high-frequency trading. Results provide an empirical confirmation of information models which theorize an accelerating effect for informed trading. To the best of the authors’ knowledge, this is the first contribution to study the impact of traders’categories at the transaction level and with different definitions of durations.

IMPLICATIONS FOR HEDGING OF THE CHOICE OF DRIVING PROCESS FOR ONE-FACTOR MARKOV-FUNCTIONAL MODELS

In this paper, we study the implications for hedging Bermudan swaptions of the choice of the instantaneous volatility for the driving Markov process of the one-dimensional swap Markov-functional model. We find that there is a strong evidence in favor of what we term "parametrization by time" as opposed to "parametrization by expiry". We further propose a new parametrization by time for the driving process which takes as inputs into the model the market correlations of relevant swap rates. We show that the new driving process enables a very effective vega-delta hedge with a much more stable gamma profile for the hedging portfolio compared with the existing ones.