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Emerging market hard-currency bonds are an asset class of growing importance, and contain exposure to an EM sovereign and the underlying industry. The authors investigate how to model this as a modification of the well-known first-to-default (FtD) basket, using the structural model, and find the approach feasible.
The pricing of derivatives tied to baskets of assets demands a sophisticated framework that aligns with the available market information to capture the intricate non-linear dependency structure among the assets. We describe the dynamics of the multivariate process of constituents with a copula model and propose an efficient method to extract the dependency structure from the market. The proposed method generates cohe…
This paper studies equity basket options -- i.e., multi-dimensional derivatives whose payoffs depend on the value of a weighted sum of the underlying stocks -- and develops a new and innovative approach to ensure consistency between options on individual stocks and on the index comprising them. Specifically, we show how to resolve a well-known problem that when individual constituent distributions of an equity index …
In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the …
In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European basket call prices. If the local volatility function is time independent then there is a closed-form expression for the approximation. Numerical tests show that the suggested approximat…
The possibility that the collective dynamics of a set of stocks could lead to a specific basket violating the efficient market hypothesis is investigated. Precisely, we show that it is systematically possible to form a basket with a non-trivial autocorrelation structure when the examined time scales are at the order of tens of seconds. Moreover, we show that this situation is persistent enough to allow some kind of f…
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expansion method to approximate the conditional expectation of the stochastic variance associated with th…
The downside risk of a portfolio of (equity)assets is generally substantially higher than the downside risk of its components. In particular in times of crises when assets tend to have high correlation, the understanding of this difference can be crucial in managing systemic risk of a portfolio. In this paper we generalize Merton's option formula in the presence jumps to the multi-asset case. It is shown how common j…
A liquidity measure based on consideration and price range is proposed. Initially defined for daily data, Liquidity Index (LIX) can also be estimated via intraday data by using a time scaling mechanism. The link between LIX and the liquidity measure based on weighted average bid-ask spread is established. Using this liquidity measure, an elementary liquidity algebra is possible: from the estimation of the execution c…
Institutional crossing platforms face a hidden-information problem: investors value trades as portfolios, but liquidity discovery is typically organized around individual securities. We model portfolio crossing as limited-communication preference elicitation over signed portfolio trades. The platform first uses price-directed demand queries to search the portfolio space and then verifies selected packages through val…
Accurately measuring portfolio similarity is critical for a wide range of financial applications, including Exchange-traded Fund (ETF) recommendation, portfolio trading, and risk alignment. Existing similarity measures often rely on exact asset overlap or static distance metrics, which fail to capture similarities among the constituents (e.g., securities within the portfolio) as well as nuanced relationships between …
Automated market makers (AMMs) are a new type of trading venues which are revolutionising the way market participants interact. At present, the majority of AMMs are constant function market makers (CFMMs) where a deterministic trading function determines how markets are cleared. Within CFMMs, we focus on constant product market makers (CPMMs) which implements the concentrated liquidity (CL) feature. In this thesis we…
We model the impact costs of a strategy that trades a basket of correlated instruments, by extending to the multivariate case the linear propagator model previously used for single instruments. Our specification allows us to calibrate a cost model that is free of arbitrage and price manipulation. We illustrate our results using a pool of US stocks and show that neglecting cross-impact effects leads to an incorrect es…
We employ a Bayesian modelling technique for high dimensional cointegration estimation to construct low volatility portfolios from a large number of stocks. The proposed Bayesian framework effectively identifies sparse and important cointegration relationships amongst large baskets of stocks across various asset spaces, resulting in portfolios with reduced volatility. Such cointegration relationships persist well ove…
Executing a basket of co-integrated assets is an important task facing investors. Here, we show how to do this accounting for the informational advantage gained from assets within and outside the basket, as well as for the permanent price impact of market orders (MOs) from all market participants, and the temporary impact that the agent's MOs have on prices. The execution problem is posed as an optimal stochastic con…
We introduce a multivariate diffusion model that is able to price derivative securities featuring multiple underlying assets. Each asset volatility smile is modeled according to a density-mixture dynamical model while the same property holds for the multivariate process of all assets, whose density is a mixture of multivariate basic densities. This allows to reconcile single name and index/basket volatility smiles in…
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European options, static hedging is implemented. It is shown that perfect hedging can be achieved. Delta and gamma…
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate framework to account simultaneously for correlations across times scales and between a basket of assets. The reported empirical results show that this extension is pertinent for fi…
Comparing DXY with an EM FX basket helps assess whether dollar strength is becoming a broader external-financing stress event for emerging markets.
DXY Index measures the U.S. dollar against a basket of major currencies and serves as a broad gauge of dollar strength and global financial conditions.
CDX HY Index tracks the cost of insuring a basket of North American high-yield corporate credit and serves as a sensitive gauge of credit risk appetite and stress.
CDX IG Index tracks the cost of insuring a basket of North American investment-grade corporate credit and is widely used as a real-time gauge of credit stress and financial conditions.
Correlation Trading — Trading implied versus realized correlation in index members.
EM FX Basket (FX).
CDX HY Index tracks the cost of insuring a basket of North American high-yield corporate credit and serves as a sensitive gauge of credit risk appetite and stress.
CDX IG Index tracks the cost of insuring a basket of North American investment-grade corporate credit and is widely used as a real-time gauge of credit stress and financial conditions.
Comparing DXY with an EM FX basket helps assess whether dollar strength is becoming a broader external-financing stress event for emerging markets.
DXY Index measures the U.S. dollar against a basket of major currencies and serves as a broad gauge of dollar strength and global financial conditions.
EM FX Basket (FX).