Hasil untuk "q-fin.PR"

Philip Z. Maymin

We derive the stochastic price process for tokens whose sole price discovery mechanism is a constant-product automated market maker (AMM). When the net flow into the pool follows a diffusion, the token price follows a constant elasticity of variance (CEV) process, nesting Black-Scholes as the limiting case of infinite liquidity. We obtain closed-form European option prices and introduce liquidity-adjusted Greeks. The CEV structure generates a leverage effect -- volatility rises as price falls -- whose normalized implied volatility skew depends only on the pool's weighting parameter, not on pool depth: Black-Scholes underprices 20%-out-of-the-money puts by roughly 6% in implied volatility terms at every pool depth, while the absolute pricing discrepancy vanishes as pools deepen. Empirically, after controlling for pool depth and flow volatility, realized return variance across 90 Bittensor subnets exhibits a strongly negative price elasticity, decisively rejecting geometric Brownian motion and consistent with the CEV prediction. A complementary delta-hedged backtest across 82 subnets confirms near-identical hedging errors at the money, consistent with the prediction that pricing differences are concentrated in the wings.

Dixon Domfeh, Saeid Safarveisi

Traditional models for pricing catastrophe (CAT) bonds struggle to capture the complex, relational data inherent in these instruments. This paper introduces CATNet, a novel framework that applies a geometric deep learning architecture, the Relational Graph Convolutional Network (R-GCN), to model the CAT bond primary market as a graph, leveraging its underlying network structure for spread prediction. Our analysis reveals that the CAT bond market exhibits the characteristics of a scale-free network, a structure dominated by a few highly connected and influential hubs. CATNet demonstrates higher predictive performance, significantly outperforming strong Random Forest and XGBoost benchmarks. Interpretability analysis confirms that the network's topological properties are not mere statistical artifacts; they are quantitative proxies for long-held industry intuition regarding issuer reputation, underwriter influence, and peril concentration. This research provides evidence that network connectivity is a key determinant of price, offering a new paradigm for risk assessment and proving that graph-based models can deliver both state-of-the-art accuracy and deeper, quantifiable market insights.

Keyuan Wu, Tenghan Zhong, Yuxuan Ouyang

We present a fast and robust calibration method for stochastic volatility models that admit Fourier-analytic transform-based pricing via characteristic functions. The design is structure-preserving: we keep the original pricing transform and (i) split the pricing formula into data-independent inte- grals and a market-dependent remainder; (ii) precompute those data-independent integrals with GPU acceleration; and (iii) approximate only the remaining, market-dependent pricing map with a small neural network. We instantiate the workflow on a rough volatility model with tempered-stable jumps tailored to power-type volatility derivatives and calibrate it to VIX options with a global-to-local search. We verify that a pure-jump rough volatility model adequately captures the VIX dynamics, consistent with prior empirical findings, and demonstrate that our calibration method achieves high accuracy and speed.

Rakhymzhan Kazbek, Yogi Erlangga, Yerlan Amanbek et al.

Computational efficiency is essential for enhancing the accuracy and practicality of pricing complex financial derivatives. In this paper, we discuss Isogeometric Analysis (IGA) for valuing financial derivatives, modeled by two nonlinear Black-Scholes PDEs: the Leland model for European call with transaction costs and the AFV model for convertible bonds with default options. We compare the solutions of IGA with finite difference methods (FDM) and finite element methods (FEM). In particular, very accurate solutions can be numerically calculated on far less mesh (knots) than FDM or FEM, by using non-uniform knots and weighted cubic NURBS, which in turn reduces the computational time significantly.

Jan Matas, Jan Pospíšil

Rough Volterra volatility models are a progressive and promising field of research in derivative pricing. Although rough fractional stochastic volatility models already proved to be superior in real market data fitting, techniques used in simulation of these models are still inefficient in terms of speed and accuracy. This paper aims to present accurate and efficient tools and techniques for Monte-Carlo simulations for a wide range of rough volatility models. In particular, we compare three commonly used simulation methods: the Cholesky method, the Hybrid scheme, and the rDonsker scheme. We also comment on the implementation of variance reduction techniques. In particular, we show the obstacles of the so-called turbocharging technique whose performance is sometimes counter-productive. To overcome these obstacles, we suggest several modifications.

Jarek Kędra, Assaf Libman, Victoria Steblovskaya

We consider an incomplete multi-asset binomial market model. We prove that for a wide class of contingent claims the extremal multi-step martingale measure is a power of the corresponding single-step extremal martingale measure. This allows for closed form formulas for the bounds of a no-arbitrage contingent claim price interval. We construct a feasible algorithm for computing those boundaries as well as for the corresponding hedging strategies. Our results apply, for example, to European basket call and put options and Asian arithmetic average options.

J. Degnan

J. Zayhowski, C. Dill

Raymond Brummelhuis, Zhongmin Luo

Absence-of-Arbitrage (AoA) is the basic assumption underpinning derivatives pricing theory. As part of the OTC derivatives market, the CDS market not only provides a vehicle for participants to hedge and speculate on the default risks of corporate and sovereign entities, it also reveals important market-implied default-risk information concerning the counterparties with which financial institutions trade, and for which these financial institutions have to calculate various valuation adjustments (collectively referred to as XVA) as part of their pricing and risk management of OTC derivatives, to account for counterparty default risks. In this study, we derive No-arbitrage conditions for CDS term structures, first in a positive interest rate environment and then in an arbitrary one. Using an extensive CDS dataset which covers the 2007-09 financial crisis, we present a catalogue of 2,416 pairs of anomalous CDS contracts which violate the above conditions. Finally, we show in an example that such anomalies in the CDS term structure can lead to persistent arbitrage profits and to nonsensical default probabilities. The paper is a first systematic study on CDS-term-structure arbitrage providing model-free AoA conditions supported by ample empirical evidence.

Alex Garivaltis

In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $θ(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their (zero-sum) game has the payoff kernel $W_θ(X)/D(X)$, where $W_θ(X)$ is the trader's final wealth and $D(X)$ is the final wealth that would have accrued to a $\$1$ deposit into the best constant-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. The resulting "universal portfolio" compounds its money at the same asymptotic rate as the best rebalancing rule in hindsight, thereby beating the market asymptotically under extremely general conditions. Smitten with this (1998) result, the present paper solves the most general tractable version of Cover and Ordentlich's (1998) max-min game. This obtains for performance benchmarks (read: derivatives) that are separately convex and homogeneous in each period's gross-return vector. For completely arbitrary (even non-measurable) performance benchmarks, we show how the axiom of choice can be used to "find" an exact maximin strategy for the trader.

Peter Carr, Zhibai Zhang

To convert standard Brownian motion $Z$ into a positive process, Geometric Brownian motion (GBM) $e^{βZ_t}, β>0$ is widely used. We generalize this positive process by introducing an asymmetry parameter $ α\geq 0$ which describes the instantaneous volatility whenever the process reaches a new low. For our new process, $β$ is the instantaneous volatility as prices become arbitrarily high. Our generalization preserves the positivity, constant proportional drift, and tractability of GBM, while expressing the instantaneous volatility as a randomly weighted $L^2$ mean of $α$ and $β$. The running minimum and relative drawup of this process are also analytically tractable. Letting $α= β$, our positive process reduces to Geometric Brownian motion. By adding a jump to default to the new process, we introduce a non-negative martingale with the same tractabilities. Assuming a security's dynamics are driven by these processes in risk neutral measure, we price several derivatives including vanilla, barrier and lookback options.

A. Stea, W. Tomlinson, T. Soong et al.

Jingchen Liu, Gongjun Xu, Z. Ying

J. Blanch, J. Robertsson, W. Symes

M. N. Hounkonnou

We build a framework for R(p;q)-deformed calculus, which pro- vides a method of computation for deformed R(p;q)-derivative and integration, generalizing known deformed derivatives and integrations of analytic functions defined on a complex disc as particular cases corresponding to conveniently cho- sen meromorphic functions. Under prescribed conditions, we define the R(p;q)- derivative and integration. Relevant examples are also given.

Y. Mizuno, M. Kumagai, S. Mattessich et al.

T. Hytönen, M. Lacey, C. P'erez

We extend the sharp weighted bound of the A2 theorem to the q‐variation norm of certain Calderón–Zygmund operators (q>2), a stronger nonlinearity than the maximal truncations that have been treated before. We obtain this result by a new non‐probabilistic approach that was independently discovered by Lerner.

Mihaly Ormos, Dusan Timotity

This paper discusses a novel explanation for asymmetric volatility based on the anchoring behavioral pattern. Anchoring as a heuristic bias causes investors focusing on recent price changes and price levels, which two lead to a belief in continuing trend and mean-reversion respectively. The empirical results support our theoretical explanation through an analysis of large price fluctuations in the S&P 500 and the resulting effects on implied and realized volatility. These results indicate that asymmetry (a negative relationship) between shocks and volatility in the subsequent period indeed exists. Moreover, contrary to previous research, our empirical tests also suggest that implied volatility is not simply an upward biased predictor of future deviation compensating for the variance of the volatility but rather, due to investors systematic anchoring to losses and gains in their volatility forecasts, it is a co-integrated yet asymmetric over/under estimated financial instrument. We also provide results indicating that the medium-term implied volatility (measured by the VIX Index) is an unbiased though inefficient estimation of realized volatility, while in contrast, the short-term volatility (measured by the recently introduced VXST Index representing the 9-day implied volatility) is also unbiased and yet efficient.

Chris Kenyon, Andrew Green

The two main issues for managing wrong way risk (WWR) for the credit valuation adjustment (CVA, i.e. WW-CVA) are calibration and hedging. Hence we start from a novel model-free worst-case approach based on static hedging of counterparty exposure with liquid options. We say "start from" because we demonstrate that a naive worst-case approach contains hidden unrealistic assumptions on the variance of the hazard rate (i.e. that it is infinite). We correct this by making it an explicit (finite) parameter and present an efficient method for solving the parametrized model optimizing the hedges. We also prove that WW-CVA is theoretically, but not practically, unbounded. The option-based hedges serve to significantly reduce (typically halve) practical WW-CVA. Thus we propose a realistic and practical option-based worst case CVA.

Abootaleb Shirvani, Stoyan V. Stoyanov, Svetlozar T. Rachev et al.

In complete markets, there are risky assets and a riskless asset. It is assumed that the riskless asset and the risky asset are traded continuously in time and that the market is frictionless. In this paper, we propose a new method for hedging derivatives assuming that a hedger should not always rely on trading existing assets that are used to form a linear portfolio comprised of the risky asset, the riskless asset, and standard derivatives, but rather should design a set of specific, most-suited financial instruments for the hedging problem. We introduce a sequence of new financial instruments best suited for hedging jump-diffusion and stochastic volatility market models. The new instruments we introduce are perpetual derivatives. More specifically, they are options with perpetual maturities. In a financial market where perpetual derivatives are introduced, there is a new set of partial and partial-integro differential equations for pricing derivatives. Our analysis demonstrates that the set of new financial instruments together with a risk measure called the tail-loss ratio measure defined by the new instrument's return series can be potentially used as an early warning system for a market crash.