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The Heston stochastic volatility model is arguably, the most popular stochastic volatility model used to price and risk manage exotic derivatives. In spite of this, it is not necessarily easy to calibrate to the market and obtain stable exotic option prices with this model. This paper focuses on the vol-of-vol parameter and its relation with the volatility of volatility index (VVIX) level. Four different approaches t…
This paper introduces SpotV2Net, a multivariate intraday spot volatility forecasting model based on a Graph Attention Network architecture. SpotV2Net represents assets as nodes within a graph and includes non-parametric high-frequency Fourier estimates of the spot volatility and co-volatility as node features. Further, it incorporates Fourier estimates of the spot volatility of volatility and co-volatility of volatil…
In stochastic Volterra rough volatility models, the volatility follows a truncated Brownian semi-stationary process with stochastic vol-of-vol. Recently, efficient VIX pricing Monte Carlo methods have been proposed for the case where the vol-of-vol is Markovian and independent of the volatility. Following recent empirical data, we discuss the VIX option pricing problem for a generalized framework of these models, whe…
We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler-Maruyama scheme. We study its asymptotic properties in the limit of a large number of time steps under a certain asymptotic regime which includes the case of finite maturity, small vol-of-vol and large initial v…
We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets. Both the asset value and the volatility processes are correlated through systemic Brownian motions, with default determined by the asset value reaching a lower boundary. We prove that if our volatility models are picked from a class of mean-reverting diffusions, the system converges as the portfolio become…
We introduce an asymptotic small noise expansion, a so called vol-of-vol expansion, for potentially infinite dimensional and rough stochastic volatility models. Thereby we extend the scope of existing results for finite dimensional models and validate claims for infinite dimensional models. Furthermore we provide new, explicit (in the sense of non-recursive) representations of the so-called push-down Malliavin weight…
We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al. (2016), which allows fast computation of up-and-out call prices for the complete set of strikes, barriers and maturities. It also utilises a novel two-states particle method to es…
The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing high-order asymptotic expansions for the at-the-money implied volatility skew, under a rich class of stochastic volatility models with independent stable-like jumps of infinite variation…
This paper attempts to explain the credit default swap (CDS) premium, using a novel approach to identify the volatility and jump risks of individual firms from high-frequency equity prices. Our empirical results suggest that the volatility risk alone predicts 48% of the variation in CDS spread levels, whereas the jump risk alone forecasts 19%. After controlling for credit ratings, macroeconomic conditions, and firms'…
Order flow is toxic when it adversely selects market makers, who may be unaware they are providing liquidity at a loss. We present a new procedure to estimate flow toxicity based on volume imbalance and trade intensity (the VPIN toxicity metric). VPIN is updated in volume time, making it applicable to the high-frequency world, and it does not require the intermediate estimation of non-observable parameters or the app…
We study market microstructure noise in high-frequency data and analyze its implications for the realized variance (RV) under a general specification for the noise. We show that kernel-based estimators can unearth important characteristics of market microstructure noise and that a simple kernel-based estimator dominates the RV for the estimation of integrated variance (IV). An empirical analysis of the Dow Jones Indu…
We revisit the problem of pricing options with historical volatility estimators. We do this in the context of a generalized GARCH model with multiple time scales and asymmetry. It is argued that the reason for the observed volatility risk premium is tail risk aversion. We parametrize such risk aversion in terms of three coefficients: convexity, skew and kurtosis risk premium. We propose that option prices under the r…
Abstract Following the “flash crash” on May 6, 2010, warning signals for impending market stress have been in high demand, yet only the VPIN metric of Easley, López de Prado, and O’Hara (ELO) has claimed success. In addition, ELO find the metric useful in predicting short-term volatility. VPIN involves decomposing volume into active buys and sells. We utilize quotes and trade data to construct an accurate trade class…
Automated Market Makers based on concentrated liquidity, such as Uniswap v3, significantly improve capital efficiency but expose Liquidity Providers (LPs) to adverse selection costs, formalized as Loss-Versus-Rebalancing (LVR). While theoretical literature quantifies these costs, the interplay between realistic blockchain microstructure and endogenous pricing mechanisms remains under-explored. This paper develops a g…
Persistent shifts in term-structure dynamics undermine the stability of single-regime models in long samples. We develop an arbitrage-free regime-switching generalized CIR (RS-GCIR) model that jointly prices the Chinese government bond (CGB) curve and corporate bond curves. To capture the systematic transmission from interest-rate conditions to credit spreads, we structure the model into two blocks and price corporat…
This paper introduces a novel stochastic model for credit spreads. The stochastic approach leverages the diffusion of default intensities via a CIR++ model and is formulated within a risk-neutral probability space. Our research primarily addresses two gaps in the literature. The first is the lack of credit spread models founded on a stochastic basis that enables continuous modeling, as many existing models rely on fa…
We provide a model that links an asset's market liquidity (i.e., the ease with which it is traded) and traders' funding liquidity (i.e., the ease with which they can obtain funding). Traders provide market liquidity, and their ability to do so depends on their availability of funding. Conversely, traders' funding, i.e., their capital and margin requirements, depends on the assets' market liquidity. We show that, unde…
The arrival of public information in the U.S. Treasury market sets off a two‐stage adjustment process for prices, trading volume, and bid‐ask spreads. In a brief first stage, the release of a major macroeconomic announcement induces a sharp and nearly instantaneous price change with a reduction in trading volume, demonstrating that price reactions to public information do not require trading. The spread widens dramat…
The 2s10s Treasury curve measures the spread between 10-year and 2-year Treasury yields and is a key indicator of growth expectations, policy path, and term structure dynamics.
Vol of Vol (Derivatives).
Vol of Vol 1M — Options and volatility market structure concept used in hedging books.
Vol of Vol 3M — Options and volatility market structure concept used in hedging books.
Vol of Vol 6M — Options and volatility market structure concept used in hedging books.
Vol of Vol 1Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 2Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 5Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 7Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 10Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 20Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 30Y — Options and volatility market structure concept used in hedging books.
Vol of Vol front — Options and volatility market structure concept used in hedging books.
Vol of Vol belly — Options and volatility market structure concept used in hedging books.
Vol of Vol long-end — Options and volatility market structure concept used in hedging books.
Vol of Vol ultra-long — Options and volatility market structure concept used in hedging books.
Vol of Vol SPX — Options and volatility market structure concept used in hedging books.
Vol of Vol NDX — Options and volatility market structure concept used in hedging books.
Vol of Vol RUT — Options and volatility market structure concept used in hedging books.
Vol of Vol SX5E — Options and volatility market structure concept used in hedging books.
Vol of Vol NKY — Options and volatility market structure concept used in hedging books.
Vol of Vol single-name — Options and volatility market structure concept used in hedging books.
Vol of Vol index — Options and volatility market structure concept used in hedging books.
Vol of Vol OTM — Options and volatility market structure concept used in hedging books.
Vol of Vol ATM — Options and volatility market structure concept used in hedging books.
Vol of Vol (Derivatives).
Vol of Vol 10Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 1M — Options and volatility market structure concept used in hedging books.
Vol of Vol 1Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 20Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 2Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 30Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 3M — Options and volatility market structure concept used in hedging books.
Vol of Vol 5Y — Options and volatility market structure concept used in hedging books.
Vol of Vol 6M — Options and volatility market structure concept used in hedging books.
Vol of Vol 7Y — Options and volatility market structure concept used in hedging books.
Vol of Vol ATM — Options and volatility market structure concept used in hedging books.
Vol of Vol belly — Options and volatility market structure concept used in hedging books.
Vol of Vol front — Options and volatility market structure concept used in hedging books.
Vol of Vol index — Options and volatility market structure concept used in hedging books.
Vol of Vol long-end — Options and volatility market structure concept used in hedging books.
Vol of Vol NDX — Options and volatility market structure concept used in hedging books.
Vol of Vol NKY — Options and volatility market structure concept used in hedging books.
Vol of Vol OTM — Options and volatility market structure concept used in hedging books.
Vol of Vol RUT — Options and volatility market structure concept used in hedging books.
Vol of Vol single-name — Options and volatility market structure concept used in hedging books.
Vol of Vol SPX — Options and volatility market structure concept used in hedging books.
Vol of Vol SX5E — Options and volatility market structure concept used in hedging books.
Vol of Vol ultra-long — Options and volatility market structure concept used in hedging books.