Equity Derivatives Research Articles

Disastrous Defaults

Abstract We define a disastrous default as the default of a systemic entity. Such an event is expected to have a negative effect on the economy and to be contagious. Bringing macroeconomic structure to a no-arbitrage asset-pricing framework, we exploit prices of disaster-exposed assets (credit and equity derivatives) to extract information on (i) the expected influence of a disastrous default on consumption and (ii) the probability of a financial meltdown. Using European data, we find that the returns of disaster-exposed assets are consistent with a systemic default being followed by a 2% decrease in consumption. The recessionary influence of disastrous defaults implies that financial instruments whose payoffs are exposed to such credit events carry substantial risk premiums. We also produce systemic risk indicators based on the probability of observing a certain number of systemic defaults or a sharp drop of consumption.

Extracting Convenience Yield Free Short-Term Interest Rates from Equity Derivatives

In this paper we use risk-free short-term interest rates (OISTIRs) derived from equity derivatives prices to make the following four contributions: (i) We introduce and compare different methods how to extract these rates and show that a method based on box spreads performs best. (ii) We compare the results with other benchmark short-term interest rates and show that OISTIRs are higher than BUND rates (30 bps for 3-month tenors), lower than EURIBOR rates (16 bps for 3-month tenors), and almost equal to EUREX repo rates. (iii) In terms of informational sensitivity we find OISTIRs to Granger-cause EURIBOR rates, at least since the year 2013. (iv) We use OISTIRs to de- rive the BUND convenience yield. We identify bond offerings and expansive monetary policy decision to negatively impact these yields, while the risk-free maturity premium has a positive impact. Finally, we think this paper may also contribute to the discussion on how to further develop EURIBOR rates.

Singular Exotic Perturbation

The Local Stochastic Volatility model is the main model used to take into account the correct pricing and hedging with the volatility dynamic. We introduce a new methodology that combines Singular perturbation analysis and exotic greek computation. We obtain asymptotic formulae for the LSV impact which work extremely well. Tests are performed on the mostly traded Autocalls in the equity derivatives business.

ANALYZING THE RELATIONSHIP BETWEEN DERIVATIVE USAGE AND SYSTEMIC RISK IN SOUTH AFRICA

This paper analyzes the relationship between derivative usage and systemic risk in South Africa. We employ expected shortfall as a measure of systemic risk for the banking sector. The more flexible Toda-Yamamoto Granger non-causality test is used to find the direction of causality between the variables, and the ARDL estimation technique is employed to estimate the specified model. We also test for the existence of a long-run relationship amongst the variables using the Bounds test approach. We find that credit derivatives and bank credit extensions increase systemic risk in the long run. Moreover, the systemic risk decreases in bank liquidity and usage of equity derivatives. However, in the short run, we find that increases in bank liquidity tend to increase systemic risk. We interpret this to imply that improvements in liquidity cause banks to undertake riskier transactions. Furthermore, the market can also perceive central bank interventions to increase liquidity as a sign of worsening financial conditions. On the backdrop of these results, we recommend continuous monitoring of derivatives markets to avoid risk excesses that could pose threat to the whole financial system.

Investors’ Preference and Regulatory Aspects in the Indian Derivatives Market

The Indian Stock market undoubtedly experienced tremendous growth in the trading activity in the last twenty-five years. The Derivatives segment of the market began its operations with the launch of Index Futures by the National Stock exchange of India (NSE) in the year 2000. The Derivatives, as a financial product, derives its value from an underlying asset and is primarily designed to reduce the risk which businesses and individuals face due to the fluctuations in the asset prices. It helps individuals and companies to undertake risky projects with high returns and use derivatives as a tool to hedge risk, which can potentially lead to wealth creation. The popular instruments of equity derivatives market are- Forward, Future, Option, and swaps. This paper presents the legal framework and regulatory aspects by the market regulator Securities and Exchange Board of India (SEBI) involving derivatives that is based on the recommendations of the L.C. Gupta Committee. SEBI laid its objectives in regulating derivative markets to ensure transparent trading environment, safety, and integrity.

Swap Rate à la Stock: Bermudan Swaptions Made Easy

We show how Markovian projection, together with some clever parameter freezing, can be used to reduce a full-fledged local volatility interest rate model – such as the Cheyette model – to a “minimal” form in which the swap rate evolved essentially like a dividend-paying stock. Using a number or numerical examples, we compare such a minimal “poor man's” model to a full-fledged Cheyette local volatility model and the market benchmark Hall–White one-factor model. Numerical tests demonstrate that the “poor man's” model is in fact sufficient to price Bermudian interest rate swaptions. The main practical implication of this finding is that – once local volatility, dividend, and short rate parameters are properly stripped from the volatility surface and interest rate curve – one can readily use the widely popular equity derivatives software for pricing exotic interest rate options such as Bermudans.

Prime Broking Default at the National Stock Exchange

When Prime Broking defaulted on its equity derivative positions at the National Stock Exchange, the central counterparty (CCP) suffered substantial losses, although there was no significant movement in the relevant market prices. This revealed hidden risks arising from collateral, liquidity and concentration, wrong-way risks and operational risks in the default management process, even when the market risk environment is benign. The CCP ends up with risks it is not designed to handle and similar to those faced by a bank. The CCP suffered massive losses, even though its market risk models functioned flawlessly.

P&L Analysis of Exotic Derivatives

In this paper, we introduce a theoretical framework to formalize the analysis of the drivers of an exotic trader's P&L (profit and loss). The framework is divided into five steps: the definition of the trading context, the choice of the hedging instruments and the choice of the valuation/hedging model are the first three steps. Once these elements are defined, the fourth step consists in breaking down the dynamic of the global P&L, including both the exotic derivative exposure and the related hedged portfolio, into specific pieces. This allows to achieve the fifth and final step whose purpose is an analysis of the residual terms of the P&L and in particular, the impact of modeling assumptions on these terms. Two illustrations are proposed to detail the approach: the first one with a generic exotic equity derivative managed with a Local Volatility model, delta-vega hedged and the second one with a generic exotic interest rate derivative managed with a Hull-White model, also delta-vega hedged. These two applications led us to propose a conjecture on the writing of the P&L for models with a single state variable and raise questions regarding the calibration of model parameters.

Liquidation Cascade and Hedging Front-Running: Evidence from the Structured Equity Product Market

We show that structured equity derivatives could cause a significant price dislocation of the underlying stock upon an event of dramatic payoff change. Moreover, one event causes another: the event cascade amplifies the magnitude of the impact. We find that a single event accounts for -6.4% return on the event day, and it increases the probability of a subsequent event by 21.3%. Given the negative price impact, traders try to liquidate ahead of each other, exacerbating the degree of price dislocation. Our results uncover the chain-reaction and (mis)coordination mechanism in complex derivatives markets that could provoke a substantial price shock.

Credit exposure under the new standardized approach for counterparty credit risk: fixing the treatment of equity options

The new standardized approach for measuring counterparty credit risk exposures (SA-CCR) will replace the existing regulatory standard methods for exposure quantification. There is an ongoing discussion with respect to the calibration and appropriate treatment of nonlinear products under the SA-CCR. The calibration of supervisory parameters for equity derivatives has been a particular bone of contention. Further, the SA-CCR struggles with the adequate reflection of nonstandard options. Our paper provides empirical evidence that the SA-CCR parameters are not aligned with historically observed volatilities. We explore a potential alignment of the SA-CCR with the new standardized approach for market risk (SA-TB) as well as the application of economic delta adjustments for path-dependent equity products. Our results demonstrate that an alignment of SA-CCR and the SA-TB could lead to a significantly improved risk assessment for equity derivatives.

Cross-Asset Market Order Flow, Liquidity, and Price Discovery

Cross-asset market activity can be a channel through which illiquidity risks originating in one market can propagate to others. This paper examines the complex intra-day linkages between the U.S. equity securities market and the equity derivatives market using high-frequency data on S&P 500 index exchange-traded funds and E-mini futures contracts. The paper finds a positive, but short-lived, relationship between the two markets' order flow activities, which relates to the supply, demand, and withdrawal of liquidity between the two markets. The paper also finds that cross-asset market order flow is a key component of liquidity and price discovery, particularly during periods of market volatility.

Assessing Contingent Convertible Bonds for Bank Recapitalization in Nigeria

This study estimates the parameters of credit derivatives, equity derivatives and structural models for bank recapitalisation in Nigeria by employing contingent convertibles (CoCos) and using the Nigeria Treasury Bill rate for 2009 as the risk-free rate, estimated recapitalisation requirements for the banks as at 2009 and relevant banks’ share prices for 2008 and 2009. The study finds the structural approach as the preferred model for CoCo pricing, as it reported the least pricing errors and also builds asset values of the banks from publicly-available quoted stock prices as well as deposit components of bank’s balance sheet information. The study also finds that CoCo bonds are likely to be fully subscribed when issued given the high stock price volatility coupled with high credit spreads in Nigeria. The paper suggests that CoCos could have been issued by the banks to recapitalise themselves without the need for regulatory actions. Therefore, usage of CoCos by banks can reduce the possibility of a bailout with public funds and lessen regulatory actions, if properly implemented, to boost the troubled banks’ capital.

A Review of Forward Starting Options Under Stochastic Numeraire

The purpose of this note is to demonstrate the impact of stochastic rates when pricing forward starting options on single asset equity derivatives. We will assume Hull-White one factor short rate model for rates with constant volatility and time dependent instantaneous volatility for the underlying.

Jump and Cojump Risk in Subprime Home Equity Derivatives

I analyze the jump frequency in the ABX index of subprime home equity credit default swaps and CME housing futures. Jumps begin to appear prior to 2007, but are more pronounced in the housing futures than the ABX. I can explain nearly 85% of the jumps from news and the housing futures. A 20 point slope in the housing futures curve leads to an expected jump of -1:4% in the BBB- ABX.

Pricing Contingent Convertibles: A Derivatives Approach

This article provides an in-depth analysis of pricing and structuring of contingent convertibles (CoCos). These debt instruments convert into the equity of the issuing bank or suffer a write-down of the face value upon the appearance of a trigger event. This trigger mechanism provides an automatic strengthening of the capital structure of the bank. Equity is in this case injected on the very moment the bank is failing to meet the minimum regulatory capital requirements or when it is heading towards a state of non-viability. In this paper the pricing of CoCos is handled using two different approaches. The first approach starts from a credit derivatives background. A second approach tackles the pricing and structuring of a CoCo as an equity derivatives problem. Both models are applied on the CoCos issued by Lloyds and Credit Suisse and allow to quantify the risks embedded within each of these structures.

The Policy Risk Premium in Equity Derivatives

This paper introduces a model that allows to measure the impact of policy risk on the dynamics of the S&P 500 index using option data. I quantify the impact of policy risk on the whole P-distribution of assets, not just on volatility, as most literature on policy risk does. I document that this type of risk is priced and has a sizeable impact on expected returns, volatilities, skewness and kurtosis. A one percent increase in the Economic Policy Uncertainty index leads to a 2.25 percentage points increase in the Equity Risk Premium.

An Intraday Trend-Following Trading Strategy on Equity Derivatives in India

In this article, we will present a trend-following based investment strategy on single-stock futures. Using the price movement of the recent past we are able to achieve a Sharpe Ratio of 1.7 on training data by cascading positions on successive positive signals and closing out positions if we hit a stop-loss. The stop-loss is computed using historical volatility. The universe is defined in an unbiased fashion to eliminate overfitting. We have used the top 75% most active single stock futures contracts and we have further filtered out products with low opening 15-minute volume. This was done to improve the scalability of the strategy. This might also help in avoiding contracts where less volatility is expected. We have trained our strategy on historical data from 2012 to 2016 and we have tested the strategy on the data from 2017 to 2018 data. Given the nature of markets in 2017-18, we have also looked at modifying the strategy to take positions more conservatively to avoid volatile situations. Empirical studies on profitable trading strategies are rare. We endeavor to shed light on the process of development of a profitable intraday trading strategy and we hope that this encourages collaboration in the active trading community.

The Determinants of CoCo Bond Prices

This study aims to empirically test how contingent convertible (CoCo) bond prices are affected by the main theoretical determinants and design features. The theoretical framework used in this article is the Equity Derivatives Model suggested by De Spiegeleer and Schoutens (2012). The authors test for the relationship between CoCo prices and key variables suggested by this model. They find that the main determinants are mostly significant and that the explanatory power of the model is high with an R-squared of 86%. The power of the model is not affected by the loss absorption mechanism (conversion to equity or principal write-down). They also identify a number of additional explanatory variables of importance.

On the application of Wishart process to the pricing of equity derivatives: the multi-asset case

Given the inherent complexity of financial markets, a wide area of research in the field of mathematical finance is devoted to develop accurate models for the pricing of contingent claims. Focusing on the stochastic volatility approach (i.e. we assume to describe asset volatility as an additional stochastic process), it appears desirable to introduce reliable dynamics in order to take into account the presence of several assets involved in the definition of multi-asset payoffs. In this article we deal with the multi asset Wishart Affine Stochastic Correlation model, that makes use of Wishart process to describe the stochastic variance covariance matrix of assets return. The resulting parametrization turns out to be a genuine multi-asset extension of the Heston model: each asset is exactly described by a single instance of the Heston dynamics while the joint behaviour is enriched by cross-assets and cross-variances stochastic correlation, all wrapped in an affine modeling. In this framework, we propose a fast and accurate calibration procedure, and two Monte Carlo simulation schemes.

Hybrid Lévy Models: Design and Computational Aspects

ABSTRACTA hybrid model is a model, where two markets are studied jointly such that stochastic dependence can be taken into account. Such a dependence is well known for equity and interest rate markets on which we focus here. Other pairs can be considered in a similar way. Two different versions of a hybrid approach are developed. Independent time-inhomogeneous Lévy processes are used as the drivers of the dynamics of interest rates and equity. In both versions, the dynamics of the interest rate side is described by an equation for the instantaneous forward rate. Dependence between the markets is generated by introducing the driver of the interest rate market as an additional term into the dynamics of equity in the first version. The second version starts with the equity dynamics and uses a corresponding construction for the interest rate side. Dependence can be quantified in both cases by a single parameter. Numerically efficient valuation formulas for interest rate and equity derivatives are developed. Using market quotes for liquidly traded assets we show that the hybrid approach can be successfully calibrated.