Latent Model Scenarios

OTCStreaming introduces OTCStreaming Latent Model Scenarios, tools designed to seamlessly integrate scenario analysis into the pricing of credit derivatives. These scenarios leverage the Latent Models introduced in OTCStreaming V2, which encapsulate hidden market variables such as default intensities across various maturities. By providing functions like survival probabilities, Latent Models form the foundation for pricing credit derivatives.

The hidden variables within the Latent Models are inferred from observable market quotes, the users' market data, through a process called Latent Model calibration. This calibration ensures that the latent models are consistently aligned with market data, enabling accurate pricing of both observable and non-observable credit derivatives.

Unlike traditional methods that define scenarios as deformations of observable market data, OTCStreaming employs a more abstract and robust approach. Credit scenarios in OTCStreaming are constructed as transformations of the survival probability function \(Q(t)\) and modifications to the loss given default. This methodology ensures consistency with the underlying latent model while providing a comprehensive view of portfolio sensitivities to default risks.

Combining deformations of survival probability and recovery scenarios accommodates a broad spectrum of credit curves, ranging from investment-grade to distressed. By focusing on the transformation of the survival probability function, this framework eliminates the need for recalibrating the Latent Model. OTCStreaming scenarios are optimized for real-time analysis of large portfolios of derivatives.

The Compound scenario represents a proportional adjustment to the cumulative hazard rate, defined as \(-\log(Q(t))\). This scenario modifies the survival probability function by applying a scaling factor \(s(t)\), resulting in a new survival probability \(Q_s(t)\):

For instance, in a Compound scenario where \(s(t) = 1.1\), the default intensities increase by 10%, approximately corresponding to a 10% widening of credit spreads. This method provides a simple yet effective way to model uniform changes in credit risk across maturities. OTCStreaming allows \(s(t)\) to be defined as either a piecewise constant or a linear function of \(t\).

The Spread scenario introduces a maturity-dependent shift factor to adjust the cumulative hazard rate. This adjustment modifies the survival probability function as follows:

Here, \(s(t)\) represents the spread adjustment function, which defines the magnitude of the shift applied to the hazard rate over time. For instance, in a Spread scenario where \(s(t) = \frac{10^{-4}}{1 - r}\) (with \(r\) being the recovery rate), the scenario simulates the sensitivity to the spread (CS01).

The Shifted scenario adjusts the cumulative hazard rate to account for the actual passage of time. This scenario modifies the survival probability function as follows:

Here, \(t_h\) represents the horizon applied to the survival probability curve. For example, in a Shifted scenario with \(t_h = 1\), the model estimates the valuation impact of holding a position by one calendar year, assuming no default occurs during this period and assuming that the survival probability curve in a year is the current curve. This approach provides a practical mechanism to evaluate the carry-roll-down effect, where the credit curve is assumed to retain its current shape over time and no default occuring over the horizon.

The elementary scenarios can be combined, being applied sequentially to create complex market scenarios. Users can define these scenarios programmatically via the API or through ioRef, the static referential framework supporting OTCStreaming. When combined with valuations, scenarios yield a vector of prices or spreads that reflect both current market conditions and the corresponding user defined market scenarios in real time. This streamlined approach enables users to efficiently analyze and consolidate portfolios in real time with consistent metrics, facilitating advanced portfolios' risks slicing and dicing.

Using market data as of May 9th, 2025, the chart above illustrates the price of Auchan's synthetic floating rate note (FRN) in black. This FRN yields a coupon of €STR + 100bps and pays the CDS auction price in the event of a credit default. For comparison, the chart also includes the corresponding values calculated using the CDS Model -referred to as the ISDA Spread- represented by the dotted lines.

The analysis incorporates the mid-market scenario as a baseline, along with two additional dilations: a 110% widening and a 90% tightening of spreads (repesctively the 110 and 090 scenarios). Furthermore, the analysis explores significant spread deformations through three key scenarios:

• Bear Scenario: The default intensity is multiplied by 2, simulating adverse market conditions, and combined with a curve flattening effect.

• Bull Scenario: The default intensity is divided by 2, reflecting favorable market conditions, and combined with a curve steepening effect.

• Carry Roll Down Scenario: The Carry Roll Down (CRD1Y) combines gain from carry and gain from roll-down effects of a steep CDS curve, assuming the FRN is held for one year. The largest gain is 5% chosing a 3Y FRN, maturiting in 2028.

This blog post illustrates how OTCStreaming V2 utilizes its Latent Model framework to perform scenario analysis. By archiving historical models over time, OTCStreaming extends this approach to enable historical scenario analysis. This feature enhances risk evaluation while providing deeper insights into market behavior. A comprehensive discussion on historical scenario analysis will be presented in an upcoming blog post.