Bounding Bermudan swaptions in a swap-rate market model

Abstract

We develop a new method for finding upper bounds for Bermudan swaptions in a swap-rate market model. By comparing with lower bounds found by exercise boundary parametrization, we find that the bounds are well within bid-offer spread. As an application, we study the dependence of Bermudan swaption prices on the number of instantaneous factors used in the model. We also establish an equivalence with LIBOR market models and show that virtually identical lower bounds for Bermudan swaptions are obtained.     

Generic market models

Currently, there are two market models for valuation and risk management of interest rate derivatives: the LIBOR and swap market models. We introduce arbitrage-free constant maturity swap (CMS) market models and generic market models featuring forward rates that span periods other than the classical LIBOR and swap periods. We develop generic expressions for the drift terms occurring in the stochastic differential equation driving the forward rates under a single pricing measure. The generic market model is particularly apt for pricing of, e.g., Bermudan CMS swaptions and fixed-maturity Bermudan swaptions.     

Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets

This paper examines whether higher order multifactor models, with state variables linked solely to underlying LIBOR‐swap rates, are by themselves capable of explaining and hedging interest rate derivatives, or whether models explicitly exhibiting features such as unspanned stochastic volatility are necessary. Our research shows that swaptions and even swaption straddles can be well hedged with LIBOR bonds alone. We examine the potential benefits of looking outside the LIBOR market for factors that might impact swaption prices without impacting swap rates, and find them to be minor, indicating that the swaption market is well integrated with the LIBOR‐swap market.     

CBDC uncertainty: Financial market implications

The current state of the art in the central bank digital currency (CBDC) literature views indexes constructed from digital currency news to be fully informed about CBDC uncertainty and its impact on the financial system. We argue that the hedging behavior of participants in the currency futures market could be more informative than CBDC uncertainty news in the presence of limited risk absorption capacity in futures markets. We show that the hedging factor has a statistically significant effect on financial market risk aversion and measures of uncertainty. The hedging behavior of currency futures market participants is informative of agents' reactions to the news and central bank policies around CBDC. Our results also show that CBDC uncertainty is a significant risk transmitter in the financial system. Hence, this characteristic makes the hedging factor even more important because it can directly impact risk aversion via its moderating effects, which later influence CBDC uncertainty.     

A displaced-diffusion stochastic volatility LIBOR market model: motivation,definition and implementation

Abstract

We present an extension of the LIBOR market model which allows for stochastic instantaneous volatilities of the forward rates in a displaced-diffusion setting. We show that virtually all the powerful and important approximations that apply in the deterministic setting can be successfully and naturally extended to the stochastic volatility case. In particular we show that (i) the caplet market can still be efficiently and accurately fit; (ii) that the drift approximations that allow the evolution of the forward rates over time steps as long as several years are still valid; (iii) that in the new setting the European swaption matrix implied by a given choice of volatility parameters can be efficiently approximated with a closed-form expression without having to carry out a Monte Carlo simulation for the forward rate process; and (iv) that it is still possible to calibrate the model virtually perfectly via simply matrix manipulations so that the prices of the co-terminal swaptions underlying a given Bermudan swaption will be exactly recovered, while retaining a desirable behaviour for the evolution of the term structure of volatilities.     

Stock index futures hedging in the emerging Malaysian market

The paper investigates hedging effectiveness of dynamic and constant models in the emerging market of Malaysia where trading information is not readily available and market liquidity is lower compared to the developed equity markets. Using daily data from December 1995 to April 2001 and bivariate GARCH(1,1) and TGARCH models, the paper uses differing variance–covariance structures to obtain hedging ratios. Performance of models is compared in terms of variance reduction and expected utility levels for the full sample period as well as the three sub-periods which encompass the Asian financial crisis and introduction of new capital control measures in Malaysia. Findings show that rankings of the hedging models change for the in-sample period depending on evaluation criteria used. TGARCH based models provide better hedging performance but only in the period of higher information asymmetry following the imposition of capital controls in Malaysia. Overall, despite the structural breaks caused by the Asian financial crisis and new capital control regulations, out of sample hedging performance of dynamic GARCH models in the Malaysian emerging market is as good as the one reported for the highly developed markets in the previous literature. The findings suggest that changes in the composition of market agents caused by large scale retreat of foreign investors following the imposition of capital control regulations do not seem to have any material impact on the volatility characteristics of the Malaysian emerging market.     

Analyzing hedging strategies for fixed income portfolios: A Bayesian approach for model selection

During the recent European sovereign debt crisis, returns on EMU government bond portfolios experienced substantial volatility clustering, leptokurtosis and skewed returns as well as correlation spikes. Asset managers invested in European government bonds had to derive new hedging strategies to deal with changing return properties and higher levels of uncertainty. In this environment, conditional time series approaches such as GARCH models might be better suited to achieve a superior hedging performance relative to unconditional hedging approaches such as OLS. The aim of this study is to test innovative hedging strategies for EMU bond portfolios for non-crisis and crisis periods. We analyze single and composite hedges with the German Bund and the Italian BTP futures contracts and evaluate the hedging effectiveness in an out-of-sample setting. The empirical analysis includes OLS, constant conditional correlation (CCC), and dynamic conditional correlation (DCC) multivariate GARCH models. We also introduce a Bayesian composite hedging strategy, attempting to combine the strengths of OLS and GARCH models, thereby endogenizing the dilemma of selecting the best estimation model. Our empirical results demonstrate that the Bayesian composite hedging strategy achieves the highest hedging effectiveness and compares particularly favorable to OLS during the recent sovereign debt crisis. However, capturing these benefits requires low transactions cost and efficiently functioning futures markets.     

Evaluating the performance of futures hedging using factors-driven realized volatility

The complexity and uncertainty of the financial market mainly stem from the rich market internal transaction information and a wide range effect of external factors. To this end, this paper proposes the combination factors-driven forecasting method to predict realized volatilities of the CSI 300 index and index futures. Based on the volatilities predicted by the proposed method, we further evaluate the ex-ante hedging performance in comparison to the conventional HAR model as well as GARCH-type models. The empirical results indicate that the factors-driven realized volatility model significantly dominates the other commonly used models in terms of hedging effectiveness. Furthermore, the superiority of the proposed method is robust in different market conditions, including significant rising or falling and abnormal market fluctuations in the COVID-19 pandemic, and in different index markets. Therefore, this paper improves the prediction accuracy of volatility by integrating market internal transaction information and external factor information, and the proposed method in this paper can be used by investors to obtain an excellent hedging effect.     

The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence

Although traded as distinct products, caps and swaptions are linked by no-arbitrage relations through the correlation structure of interest rates. Using a string market model, we solve for the correlation matrix implied by swaptions and examine the relative valuation of caps and swaptions. We find that swaption prices are generated by four factors and that implied correlations are lower than historical correlations. Long-dated swaptions appear mispriced and there were major pricing distortions during the 1998 hedge-fund crisis. Cap prices periodically deviate significantly from the no-arbitrage values implied by the swaptions market.     

Selective hedging strategies for crude oil futures based on market state expectations

This paper studies the ex-ante selective hedging strategies of crude oil futures contracts based on market state expectations and compares the hedging performances to the traditional minimum variance routine hedging strategies. The main advantage of the proposed method is that it achieves a trade-off between return and risk, rather than hedges risk at all costs. Specifically, we first use a multi-input Hidden Markov Model(HMM) to identify the market state, assess the market’s herding impact, and then integrate the findings of identification and measurement to forecast the price trend. We offer an adjustment criterion for the hedge ratios driven by GARCH²-type models based on the anticipated market state. We conducted an empirical analysis to examine the hedging effect of WTI and Brent crude oil futures, the results indicate that the proposed state-dependent hedging strategies are superior to the traditional model-driven hedging strategies concerning the hedged portfolio based on four criteria. The robustness check reveals that the proposed hedging strategies still outperform in different market situation. The findings can help traders in the crude oil markets, and the methodology can be applied to other energy markets.     

A perturbative approach to Bermudan options pricing with applications

In this paper we address the problem of the valuation of Bermudan option derivatives in the framework of multi-factor interest rate models. We propose a solution in which the exercise decision entails a properly defined series expansion. The method allows for the fast computation of both a lower and an upper bound for the option price, and a tight control of its accuracy, for a generic Markovian interest rate model. In particular, we show detailed computations in the case of the Bond Market Model. As examples we consider the case of a zero coupon Bermudan option and a coupon bearing Bermudan option; in order to demonstrate the wide applicability of the proposed methodology we also consider the case of a last generation payoff, a Bermudan option on a CMS spread bond.     

The hedging effect of green bonds on carbon market risk

This paper explores effective hedging instruments for carbon market risk. Examining the relationship between the carbon futures returns and the returns of four major market indices, i.e., the VIX index, the commodity index, the energy index and the green bond index, we find that the connectedness between the carbon futures returns and the green bond index returns is the highest and this connectedness is extremely pronounced during the market's volatile period. Further, we develop and evaluate hedging strategies based on three dynamic hedge ratio models (DCC-APGARCH, DCC-T-GARCH, and DCC-GJR-GARCH models) and the constant hedge ratio model (OLS model). Empirical results show that among the four market indices the green bond index is the best hedge for carbon futures and performs well even in the crisis period. The paper also provides evidence that the dynamic hedge ratio models are superior to the OLS model in the volatile period as more sophisticated models can capture the dynamic correlation and volatility spillover between the carbon futures and market index returns.     

Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis

We empirically compare Libor and Swap Market Models for the pricing of interest rate derivatives, using panel data on prices of US caplets and swaptions. A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices. For both models we analyze how well they price caplets and swaptions that were not used for calibration. We show that the Libor Market Model in general leads to better prediction of derivative prices that were not used for calibration than the Swap Market Model. Also, we find that Market Models with a declining volatility function give much better pricing results than a specification with a constant volatility function. Finally, we find that models that are chosen to exactly match certain derivative prices are overfitted; more parsimonious models lead to better predictions for derivative prices that were not used for calibration.     

Corporate Hedging Policy and Equity Mispricing

We show that firms’ use of derivatives is negatively associated with stock mispricing. This result is consistent with the notion that hedging improves the transparency and predictability of firms’ cash flows resulting in less misvaluation. Furthermore, we show that the negative relationship between mispricing and hedging is particularly strong when market value is below fundamental value, which is consistent with prior evidence that hedging has a positive impact on firm valuation. Finally, we provide evidence that a “spread‐out” hedging policy that entails the use of a variety of derivative contracts can be more effective in reducing mispricing.     

Dynamic Hedging Effectiveness in South Korean Index Futures and the Impact of the Asian Financial Crisis

This paper focuses on the impact of the 1997 Asian financial market crisis upon hedging effectiveness within the KOSPI 200 stock index and index futures markets. The paper utilizes the inter-temporal relationship between the two markets to examine the characteristics of several minimum variance hedge ratios. It also examines the performances of alternative hedging strategies for dynamic portfolio management in the presence of cointegrated time-varying risks. The results show a decline in the persistence of conditional volatility within market prices after the crisis. This decline leads to the relative performance of utilizing constant hedge ratios to increase, though not significantly so to guarantee a superior performance over more sophisticated time-varying hedge ratio strategies.     

Option trading and individual investor performance

This paper examines the impact of option trading on individual investor performance. The results show that most investors incur substantial losses on their option investments, which are much larger than the losses from equity trading. We attribute the detrimental impact of option trading on investor performance to poor market timing that results from overreaction to past stock market returns. High trading costs further contribute to the poor returns on option investments. Gambling and entertainment appear to be the most important motivations for trading options while hedging motives only play a minor role. We also provide strong evidence of performance persistence among option traders.     

Delta-hedging correlation risk?

While the Gaussian copula model is commonly used as a static quotation device for CDO tranches, its use for hedging is questionable. In particular, the spread delta computed from the Gaussian copula model assumes constant base correlations, whereas we show that the correlations are dynamic and correlated to the index spread. It might therefore be expected that a dynamic model of credit risk, which is able to capture the dependence between the base correlations and the index spread, will have better hedging performances. In this paper, we compare delta hedging of spread risk based on the Gaussian copula model, to the implementation of jump-to-default ratio computed from the dynamic local intensity model. Theoretical and empirical analysis are illustrated by using the market data in both before and after the subprime crisis. We observe that delta hedging of spread risk outperforms the implementation of jump-to-default ratio in the pre-crisis period associated with CDX.NA.IG series 5, and the two strategies have comparable performance for crisis period associated with CDX.NA.IG series 9 and 10. This shows that, although the local intensity model is a dynamic model, it is not sufficient to explain the joint dynamic of the index spread and the base correlations, and a richer dynamic model is required to obtain better hedging results. Moreover, although different specifications of the local intensity can be fitted to the market data equally well, their hedging results can be significant different. This reveals substantial model risk when hedging CDO tranches.     

HEDGING PERFORMANCE AND HEDGING OBJECTIVES: TESTS OF NEW PERFORMANCE MEASURES IN THE FOREIGN CURRENCY MARKET

Two related approaches are introduced for measuring the performance of hedging strategies. The first summarizes the risk-return trade-off as a single annotated numerical value, and the second displays it as a performance curve. Two bounded sets of hedging strategies are used to evaluate empirically the performance measures. One set is divided according to whether it best satisfies short or long hedging objectives. Results show that market conditions often provide opportunities to reduce variance and increase expected return. They also suggest that the Commodity Futures Trading Commission's typical definition of “bona fide” hedging should be reconsidered.