Variance-Optimal Hedging in General Affine Stochastic Volatility Models

In this paper, we present some results on Geometric Asian option valuation for affine stochastic volatility models with jumps. We shall provide a general framework into which several different valuation problems based on some average process can be cast, and we shall obtain closed form solutions for some relevant affine model classes.

A semi-analytic pricing formula for lookback options under a general stochastic volatility model

Estimation of continuous-time stochastic volatility models with jumps using high-frequency data

We characterize the behavior of the Rough Heston model introduced by Jaisson and Rosenbaum (2016, Ann. Appl. Probab., 26, 2860–2882) in the small‐time, large‐time, and (i.e., ) limits. We show that the short‐maturity smile scales in qualitatively the same way as a general rough stochastic volatility model , and the rate function is equal to the Fenchel–Legendre transform of a simple transformation of the solution to the same Volterra integral equation (VIE) that appears in El Euch and Rosenbaum (2019, Math. Financ., 29, 3–38), but with the drift and mean reversion terms removed. The solution to this VIE satisfies a space–time scaling property which means we only need to solve this equation for the moment values of and so the rate function can be efficiently computed using an Adams scheme or a power series, and we compute a power series in the log‐moneyness variable for the asymptotic implied volatility which yields tractable expressions for the implied vol skew and convexity which is useful for calibration purposes. We later derive a formal saddle point approximation for call options in the Forde and Zhang (2017) large deviations regime which goes to higher order than previous works for rough models. Our higher‐order expansion captures the effect of both drift terms, and at leading order is of qualitatively the same form as the higher‐order expansion for a general model which appears in Friz et al. (2018, Math. Financ., 28, 962–988). The limiting asymptotic smile in the large‐maturity regime is obtained via a stability analysis of the fixed points of the VIE, and is the same as for the standard Heston model in Forde and Jacquier (2011, Finance Stoch., 15, 755–780). Finally, using Lévy's convergence theorem, we show that the log stock price tends weakly to a nonsymmetric random variable as (i.e., ) whose moment generating function (MGF) is also the solution to the Rough Heston VIE with , and we show that tends weakly to a nonsymmetric random variable as , which leads to a nonflat nonsymmetric asymptotic smile in the Edgeworth regime, where the log‐moneyness as , and we compute this asymptotic smile numerically. We also show that the third moment of the log stock price tends to a finite constant as (in contrast to the Rough Bergomi model discussed in Forde et al. (2020, Preprint) where the skew flattens or blows up) and the process converges on pathspace to a random tempered distribution which has the same law as the hyper‐rough Heston model, discussed in Jusselin and Rosenbaum (2020, Math. Finance, 30, 1309–1336) and Abi Jaber (2019, Ann. Appl. Probab., 29, 3155–3200).

A Hybrid Asymptotic Expansion Scheme: An Application to Long-Term Currency Options

In this paper we consider the range of prices consistent with no arbitrage for European options in a general stochastic volatility model. We give conditions under which the infimum and the supremum of the possible option prices are equal to the intrinsic value of the option and to the current price of the stock, respectively, and show that these conditions are satisfied in most of the stochastic volatility models from the financial literature. We also discuss properties of Black–Scholes hedging strategies in stochastic volatility models where the volatility is bounded.

The Smile in Stochastic Volatility Models

Risk premium and fair option prices under stochastic volatility: the HARA solution

We develop an efficient Monte Carlo method for the valuation of financial contracts on discretely realized variance. We work with a general stochastic volatility model that makes realized variance dependent on the full path of the asset price. The variance contract price is a high-dimensional integral over the fundamental sources of randomness. We identify a two-dimensional manifold that drives most of the uncertainty in realized variance, and we compute the contract price by combining precise integration over this manifold, implemented as fine stratification or deterministic sampling with quasirandom numbers, with conditional Monte Carlo on the remaining dimensions. For a subclass of models and a class of nonlinear payoffs, we derive approximate theoretical results that quantify the variance reduction achieved by our method. Numerical tests for the discretized versions of the widely used Hull–White and Heston models show that the algorithm performs significantly better than a standard Monte Carlo, even for fixed computational budgets.

An approximation of small-time probability density functions in a general jump diffusion model

<p>This study aimed to test the effect of macroeconomic factors on the movements of stock prices of Jordanian industrial companies listed in Amman Stock Exchange (ASE) in order to provide empirical evidence about the determinants of the movements of stock prices. To achieve this objective, all the 77 Jordanian industrial firms listed at ASE for fifteen years from 2000 to 2014 have been selected, resulting in 1054 firm-year observations. The unbalanced pooled cross-sectional time series multiple least square regression method has been used to present data analysis. while the experiential results showed significant negative effect of two of the macroeconomic factors, namely, interest and inflation rates, on the movements of the Jordanian industrial companies stock prices, results found that the effect of money supply and GDP on the movements of stock prices were significantly positive. These results are consistent with (Mukherjee and Naka, 1995, Zhao, 1999 & Udegbunam and Eriki, 2001, Al-Qenae, Li & Wearing, 2002, Dimitrios Tsoukalas, 2003 , Ibrahim 2003; Chaudhuri and Smiles, 2004)</p>

The capital market plays a crucial role in economic growth, serving as a platform for investors and companies to engage in financial transactions. One of the key factors investors consider when making investment decisions is stock price movement, which various financial ratios can influence. This study examines the effect of Return on Assets (ROA), Current Ratio (CR), and debt-to-equity ratio (DER) on stock prices at PT. Unilever Indonesia Tbk over the period 2014-2023. This research employs a quantitative method with a descriptive and verification approach, utilizing secondary data from the company's financial reports and stock price data from the Indonesia Stock Exchange (IDX). The purposive sampling method was used to select data, and analysis was conducted using multiple linear regression. The study also conducted classical assumption tests, including normality, heteroscedasticity, multicollinearity, and autocorrelation tests, to ensure the validity of the results. The findings reveal that ROA, CR, and DER do not significantly affect stock prices, either partially or simultaneously. This contradicts several previous studies that suggested a strong correlation between financial ratios and stock prices. The results indicate that stock price fluctuations at PT. Macroeconomic conditions, market sentiment, and external shocks may influence Unilever Indonesia Tbk. In conclusion, this study suggests that investors should consider additional factors beyond financial ratios when investing in the Fast Moving Consumer Goods (FMCG) sector. Future research should explore the impact of external factors, including inflation, interest rates, and industry trends, on stock price movements.

We perform robust bilateral Granger causality tests for the US stock prices, home prices, and private consumption. The robust test procedures involve the use of recently developed time series analysis of non-stationary data with possible structural breaks. We find the underlying data to be generally non-stationary and non-cointegrated. The empirical results indicate the presence of bilateral causality between stock prices and home prices and between stock prices and consumer spending. The results show unilateral causality from home prices to consumer spending. Our findings support the reinforcing effects of stock and home price movements on private consumption, as well as the feedback effect of consumer spending on stock prices.

In the world of capital markets, indicators are used to measure changes in stock prices. A stock index is an indicator to see information about stock price movements. The existence of various information both from within the country and abroad is one of the external factors that causes the movements of stock prices to change significantly. This study aims to analyze the price movements of the companies' shares included in the LQ45 Index from the impact of a big event that is currently happening, namely the pandemic Covid-19. This study uses the method of Survival Analysis with the approach Kaplan Meier, variable of this study uses stock prices. The results of the research that have been conducted found that external factors, namely information about Covid-19 that spread throughout the world, given a negative impact on stock price movements on the LQ45 Index, namely 45 LQ45 companies experienced a decline in stock prices during the observation period, 5 of 45 companies still experienced a declined. After the observation period took place, viewed by sector, eight sectors included in LQ45 experienced a decline in stock prices at the same time during the period 02 January to 31 March 2020.

There are two opposing hypotheses regarding the informative role of stock prices. The first hypothesis argues that the stock market is merely a sideshow where security prices reflect the consequences of managers’ decisions for firms’ cash flows but do not influence them. In other words, trading in secondary markets has no direct impact on firms’ decisions. The second, known as the “active informant hypothesis”, states that security prices influence managers’ real decisions because some investors trade on private information not available to managers, who therefore rely on stock prices as a source of information. There is recent evidence supporting the latter hypothesis. In order to help elucidate this current debate, this dissertation examines the stock price informativeness of firms facing a product market threat and competition from their peers. I reason that when facing a threat, managers of firms tend to be more inquisitive about their price stock movements and also about the stock price movements of their peers. Indeed, my empirical analyses show that managers of firms facing higher product market threat and competition are more sensitive to the information contained in their stock prices. I also find that firms learn more from their peers’ stock price movements as the level threat is greater except when the threat is at its highest level.