NN² Capital

Designing and managing quantitative strategies

Director and Hedge Fund Manager

Harbourfront Technologies

•	Advised CFOs and VPs of finance on valuing complex derivatives
•	Built models for for assessing credit risks embedded in debt offerings
•	Performed Monte-Carlo simulations for pricing performance share units
•	Developed a reverse dispersion volatility strategy for an asset management firm
•	Implemented backtest and stress-test methodologies for hedge funds
•	Built a database for stocks and options. Implemented statistical and volatility arbitrage strategies using the database
•	Implemented models and Matlab programs for advanced modeling of the volatility skew and term structure
•	Developed a 2-factor options pricing model for valuing and hedging commodity portfolios
•	Mentored junior doctorates. Provided advice and guidance for a career in quantitative finance

Quantitative Strategist

PRMIA - Professional Risk Managers'​ International Association

•	Coordinated and organized finance and risk management conferences
•	Assumed responsibility for sponsorship and communication
•	Worked as the editor for PRMIA Toronto newsletter. Readership: 6800 members

Steering Committee Member

•	Performed derivative valuation for clients. Specialized in complex structured products
          -Equities: Asian quanto basket options, variance swaps, total return swaps, convertible bonds, rainbow options, equity-linked note
          -Fixed income: exotic interest rate swaps, commercial mortgage pools, mortgage back securities, convertible bonds, term loans
         -Structured credits: credit default swaps, collateralized debt obligation, credit-linked notes, total return swaps
        -Commodities: commodity swaps, commodity options
        -Foreign exchange: FX forwards and options
        -Other: catastrophe bonds, ABCP, performance share units
•	Advised banks on constructing discount factor curves used to value interest rate derivatives: vanilla curves, cross-currency curves, overnight index swap curves
•	Reviewed hedging strategies for hedge accounting purposes
•	Managed major clients of the firm and generated consistent consulting revenue 
•	Supervised a team of junior and senior analysts. Trained and mentored less experienced members of the group

Quantitative Analyst, Manager

Ernst Young Financial Advisory

•	Developed computer programs based on binomial trees and Monte Carlo simulation to value exotic derivatives such as convertible bonds, executive stock options
•	Performed credit value adjustments (CVA) for OTC derivatives
•	Reviewed and vetted quantitative risk management systems: market, credit, operational, liquidity risks
•	Calculated Value at Risks (credit, operational, market) using analytical and historical simulation methods
•	Developed models for loan loss provisions and Economic Capital of retail credit card and mortgage portfolios
•	Advised banks on retail PD, EAD, LGD models
•	Reviewed a bank’s credit portfolio management and developed score cards for its retail and commercial lending

Senior Quantitative Analyst

Université Laval

-Designed hedging strategies for managing the risks of a portfolio of credit derivatives

Research Assistant

Université de Sherbrooke

-Conducted research in life science using supercomputer clusters (+5000 CPU high performance computing)
-Analyzed large data sets with the help of parallel supercomputers
-Workshops in parallel computing and financial mathematics

Postdoctoral Researcher

We help Asset Managers, Chief Financial Officers deal with complex issues of financial derivatives:

-Modeling and pricing of complex derivatives such as convertible bonds, mortgage backed securities, variance swaps, credit default swaps, collateral debt obligation
-Performing Monte Carlo simulation to value executive stock options and real options
-Yield curve construction (LIBOR, overnight index swap, cross currency) in various currencies
-Development of a structural credit model for determining corporate credit spreads and probabilities of default
-Implementation of advanced derivative pricing models
-Independent Price Verification
-General derivative related consulting services


We help portfolio managers, hedgers, traders better manage the risks and extract alpha:

-Risk analytics for derivatives books such as calculation of the Greeks, Value at Risk
-Validation of risk management models such as Economic Capital, IFRS9
-Implementation of advanced options pricing models: stochastic volatility, local volatility
-Development of multi-factor stochastic models for volatility and commodity related products
-Design and implementation of database for financial data and analytics
-Developing trading and hedging strategies for equity and commodity portfolios

Feel free to connect with me on LinkedIN

Fractional Geometric Brownian Motion and Its Application to Futures Arbitrage

The paper proposed an extension to the Geometric Brownian Motion based on fractional Brownian motion (FBM), which incorporates trend fractal dimensions (FTD)—distinguishing between upward (D⁺) and downward (D⁻) dimensions—combined with momentum lifecycle theory.

It constructed a futures pricing model and designed an arbitrage strategy based on the futures–cash basis. 

Findings
-The study introduces a dynamic arbitrage strategy based on fractal principles that significantly outperforms conventional static-threshold methods in both profitability and risk control.

-The strategy leverages trend fractal dimensions (D⁺ and D⁻) and momentum lifecycle logic to adapt to the evolving structure of the basis.

-Backtesting shows that the fractal strategy achieved a net total return of 12.71%, compared to 7.06% for the traditional approach.

-It also produced a positive after-cost Sharpe ratio of 0.32, indicating genuine risk-adjusted profitability, while the traditional strategy recorded a negative Sharpe ratio of −0.61, making it economically unviable.

-During a stress test simulating the 2015 market crash, the fractal strategy showed strong resilience.

-While the buy-and-hold approach suffered major losses and the traditional arbitrage strategy lost −5.82%, the fractal strategy limited its drawdown to −0.83%, nearly breakeven.

-This robustness under extreme market conditions highlights the strategy’s effectiveness for capital preservation and its superior performance stability.

Reference: Xu Wu and Yi Xiong, A fractal market perspective on improving futures pricing and optimizing cash-and-carry arbitrage strategies, Quantitative Finance and Economics, Volume 9, Issue 4, 713–744.

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#derivatives #trading #arbitrage

ABSTRACT
Traditional futures pricing models, based on the efficient market hypothesis, often fail in today’s complex financial markets, leading to significant pricing errors and unreliable arbitrage strategies. This study posits that the fractal market hypothesis (FMH) offers a superior framework by accounting for long memory and multi-scale dynamics. Methodologically, we developed a fractal futures pricing model by incorporating the Hurst exponent and constructed a novel cash-futures arbitrage strategy using trend fractal dimensions and momentum lifecycle logic to generate dynamic trading signals. Empirical analysis using CSI 300 data demonstrates that our fractal pricing model significantly reduces pricing errors compared to the traditional cost-of-carry model. Furthermore, the proposed fractal-based arbitrage strategy achieves substantially higher returns, superior risk-adjusted performance, and lower drawdowns than conventional threshold-based approaches, showing robustness across diverse market conditions...

Nam Nguyen, Ph.D.

Quantitative Strategist and Derivatives Specialist

The Effectiveness of Dollar Cost Averaging (DCA) Under Varying Market Conditions

DCA has often been presented as an effective portfolio management technique, and financial advisors and brokers encourage clients to adopt it. But is it truly effective, or merely a marketing scheme?

The paper examined the effectiveness of DCA. It employed Monte Carlo simulation, rather than historical backtesting.

Findings
-The study examines how market volatility influences the performance of the Dollar-Cost Averaging strategy, which invests a fixed amount periodically.

-Monte Carlo simulations are used to compare DCA with the Buy and Hold (B&H) strategy under different market conditions.

-The analysis considers the effects of market drift, volatility, and transaction frequency on returns.

-Results indicate that DCA performs better than B&H in highly volatile markets.

-In contrast, B&H produces higher returns in stable market environments.
Reducing the frequency of investments improves the performance of DCA.

-The findings suggest that DCA’s effectiveness depends on market volatility and investment frequency.

-The study provides practical insights for investors on how to optimize DCA based on market characteristics.

Reference: Siyuan Sang, Ru Bai, Haibo Li, The Dynamic Relationship Between Market Volatility and Dollar Cost Averaging Strategy Returns: An Empirical Investigation, in Proceedings of the 2025 3rd International Academic Conference on Management Innovation and Economic Development (MIED 2025)

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#portfoliomanagement #quantitativeresearch #investing

ABSTRACT
This study empirically examines the performance of a Dollar-Cost Av-
eraging (DCA) strategy under varying market volatility conditions. DCA, which involves investing a fixed sum at regular intervals, is popular for its risk-mitigation properties. However, its effectiveness, especially relative to lump-sum investing (B&H)—depends on market  dynamics. Using Monte  Carlo simulations to generate price paths based on geometric  Brownian motion, we analyze DCA returns,  volatility  clustering,  and  transaction  frequency.  Results  indicate  that while DCA underperforms  B&H in steadily rising markets, it can offer risk-adjusted advantages in highly volatile scenarios. The study also discusses practical implications for optimizing DCA by adjusting investment frequency and considering transaction costs.

Return and Variance Risk Premia in the Bitcoin Market

The paper investigates the Bitcoin return premium (BP) and the Bitcoin variance risk premium (BVRP).

The authors utilized Bitcoin options data traded on Deribit from July 2017 to December 2022 to calculate the BVRP. The implied variance is computed using the same methodology as the VIX index. 

Findings
-The study finds that the Bitcoin premium (BP) is substantially higher than that of traditional assets such as currencies, commodities, and equities, averaging around 66% annually.

-The annualized risk-neutral variance (BVIX²) and physical realized variance (BRV) are 0.72 and 0.58, respectively, resulting in a variance risk premium (VRP) of 0.14, which is notably higher than the S&P 500’s estimated 0.02.

-Conditional analysis across market regimes shows that BP is higher during the high-volatility (HV) regime, corresponding with generally higher option price premia.

-The low-volatility cluster, however, exhibits a higher VRP (0.17) than the high-volatility cluster (0.12), suggesting a disconnect between variance and VRP.

-The results reveal a negative relationship between BP and BVRP in the Bitcoin market, contrasting with the positive relationship observed in the S&P 500.

-Clustering results also indicate a positive relationship between returns and variance, supporting the inverse leverage effect hypothesis.

Reference: Caio Almeida, Maria Grith, Ratmir Miftachov, Zijin Wang, Risk Premia in the Bitcoin Market, arXiv:2410.15195

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#bitcoin #volatility #riskmanagement

ABSTRACT
We analyze the first and second moment risk premia in the Bitcoin market based on options and realized returns and contrast them to the premia embedded in the main US stock index market. First, Bitcoin is much more volatile and has a higher variance risk premium than the S&P 500. By decomposing the return premium into different regions of the return state space, we find that while most of the S&P 500 equity premium comes from mildly negative returns, the corresponding negative Bitcoin returns (between three and one standard deviations) account for only one-third of the total Bitcoin premium (BP). Further, applying a novel clustering algorithm to a collection of estimated Bitcoin option-implied risk-neutral densities, we find that risk premia vary over time as a function of two distinct market volatility regimes. The low-volatility regime implies a relatively high share of BP attributable to positive returns and a high Bitcoin Variance Risk Premium (BVRP). In high-volatility states, the BP attributable to positive and negative returns is more balanced, and the BVRP is lower. These results suggest Bitcoin investors are more concerned about variance and upside risk in a low-volatility regime.

Incorporating Reflexivity into the Black–Scholes-Merton Framework

The paper incorporates reflexivity into the BSM framework. It proposes three modifications:

1-Predictability of Brownian motion: Trader dependence on predictive models induces path dependence, breaking the martingale property of the Wiener process.

2-Drift coefficient deviation from risk free rate: Large-scale institutional model use shifts the drift away from the risk-free rate by a reflexivity-induced term.

3-Volatility endogeneity: The volatility at time t depends on lagged volatility and hedging intensity.

Findings
-The paper extends the Black–Scholes model by incorporating reflexivity, showing how feedback mechanisms from model-based trading influence asset price dynamics.

-It modifies the drift, diffusion, and volatility terms to reflect the effects of widespread use of quantitative trading models.

-The proposed framework challenges three assumptions of classical financial theory:
i) The risk-neutral drift equals the risk-free rate.
ii) Volatility is exogenous.
iii) Markets are complete.

-The model presents a more realistic depiction of modern markets, where collective model-driven behavior affects the variables within pricing models.

-It highlights that reflexivity amplifies systemic risk and market fragility, providing a structural explanation for extreme financial events.

Reference: Atharva Singh Rathore, Reflexivity in Financial Markets: A Theoretical Framework Extending the Black–Scholes Model, 2025

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#options #volatility #derivatives

ABSTRACT
Extensive research has been conducted on the creation of models to predict market movement, with the Black-Scholes model being a cornerstone. The Black-Scholes model has been an integral part of modern financial theory, providing a mathematical framework for option prices under the assumption of exogenous market dynamics. However, in practice, financial markets are reflexive: Trading strategies based on mathematical models take as input the very variables that were affected by investing using these models. This challenges the core assumption of market efficiency in traditional financial theory. This research proposes a framework to formally introduce reflexivity into the Black-Scholes model. Specifically, we explore three mechanisms through which reflexivity alters market dynamics: (i) predictability of Brownian motion when trader dependence on mathematical model introduces path dependence, (ii) deviation of the drift coefficient from risk-free rate in a risk-neutral world due to large-scale institutional model use, and (iii) endogeneity of volatility....

Impact of Artificial Intelligence on Financial Markets: a Quantitative and Qualitative Analysis

The paper examined the impact of AI on trading and risk management, performing both quantitative and qualitative analyses. 

Findings
-It explains that AI has significantly influenced algorithmic trading and the broader financial markets.

-AI has enhanced market efficiency, order execution, and decision-making accuracy by enabling real-time data analysis at unprecedented levels.

-Technological advances driven by AI have improved market liquidity and operational performance, as AI systems surpass humans in trade execution speed and precision.

-AI also enhances predictive accuracy, helping traders and investors develop strategies and manage risks more effectively.

-However, integrating AI into trading systems introduces new risks to market stability.

-Concerns include flash crashes—sudden and sharp price declines caused by algorithmic errors—and systemic risks, where the failure of one AI system could trigger cascading failures across interconnected systems.

Reference: Neeraj Kahol Sharma, Assessing the AI Impact on Financial Markets through Algorithmic Trading, Journal of Basic Science and Engineering, Vol. 22, No. 1, (2025)

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#trading #machinelearning #artificialintelligence

ABSTRACT
This paper attempts to analyze the effects of AI algorithmic trading on the financial markets. The brakes of algorithmic trading are being transcended by the evolution of machine learning, deep learning technologies, and even reinforced learning. The evolution of AI poses ethical issues in addition to market volatility and systemic risk. My approach combines qualitative and quantitative analyses to evaluate the magnitude of improvements in the efficiency of the trading system with the implementation of AI compared to legacy systems. The results of the analysis show that the concerns of regulators with emerging AI technologies are indeed warranted; but the positive impacts AI technologies bring to the performance of markets are difficult to dismiss. This paper suggests the development of algorithms for trading with AI systems to enhance control, transparency, and governance.

Volatility Risk Premium Around Macroeconomic Announcements

The paper examined the returns of delta-neutral straddles around macroeconomic announcements. By analyzing these returns, one can draw conclusions about the volatility risk premium (VRP) on announcement dates.

Findings
-The study found negative returns across all event windows, weighting methods, and macroeconomic announcements.

-There is no evidence that buying straddles before macroeconomic announcements generates profits.

-A comparison between all trading days and macroeconomic announcement days was performed to examine whether straddles are priced differently during announcements.

-Equal-weighted results show that straddles on macroeconomic announcement days yield lower returns than those on all days.

-Value-weighted results are mixed, with straddles on announcement days sometimes outperforming and sometimes underperforming the full sample.

-Volume-weighted straddles on announcement days outperform straddles on all days across all event windows.

-Returns for specific announcements such as FOMC, CPI, and PPI are lower than the equal-weighted average returns across all announcements.

-This suggests that the risk associated with options around these specific macroeconomic events may have been overestimated.

-Future research could examine the impact of adding or excluding different macroeconomic indicators to assess whether event-specific effects vary.

Reference: Carl Windmar, Risk Premium around Macroeconomic Announcements, Evidence from Delta-Neutral Straddles, Lund University, 2025

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#vix #volatility #riskmanagement

ABSTRACT
This paper analysed the returns on delta-neutral straddles around macroeconomic announcements. The results for straddles on all macroeconomic events were negative returns across all weighting methods and across the majority of holding periods. Furthermore, the returns for individual macroeconomic data announcements were negative, except for money supply and employment data which showed inconclusive results. Therefore, there is no evidence of consistent underestimation of risk that can be exploited. The empirical results confirm the theory behind straddle returns.

Hedge Effectiveness Under a Four-State Regime Switching Model

Machine learning methods often face challenges of interpretability, overfitting, and a lack of robustness in real-world deployment.

The paper proposed a more “classical” regime identification technique. It developed a four-state regime switching (PRS) model for FX hedging.

Findings
-The authors develop a four-state regime-switching model using forward contracts to hedge foreign exchange positions.

-The PRS model reduces portfolio variance more effectively than existing hedging strategies in the dollar, euro, yen, and lira markets.

-In the rupee market, the model delivers the second-best performance among tested approaches.

-The results suggest that optimizing the memory level in the four-state regime-switching model produces better hedging outcomes than applying a constant hedge ratio across the entire period.

-The findings align with prior research advocating for models that update with more recent data over time.

-The superior performance of the proposed model relative to other dynamic approaches indicates its ability to capture asymmetry and fat-tail characteristics common in FX returns.

-The particularly strong results for the lira imply that the model is especially effective for highly volatile currencies.

-The model adjusts the estimation horizon dynamically, allowing it to determine the optimal hedge ratio under prevailing market conditions.

Reference: Taehyun Lee, Ioannis C. Moutzouris, Nikos C. Papapostolou, Mahmoud Fatouh, Foreign exchange hedging using regime-switching models: The case of pound sterling, Int J Fin Econ. 2024;29:4813–4835.

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#hedging #riskmanagement #portfoliomanagement

ABSTRACT
We develop a four-state regime-switching model for optimal foreign exchange (FX) hedging using forward contracts. The states correspond to four distinct market conditions, each defined by the direction and magnitude of deviation of the prevailing FX spot rate from its long-term trends. The model's performance is evaluated for five currencies against the pound sterling for various horizons. Our examination compares the hedging outcomes of the proposed model to those of other commonly employed hedging methods. The empirical results suggest that our model demonstrates the highest level of risk reduction for the US dollar, euro, Japanese yen and Turkish lira and the second-best performance for the Indian rupee. The risk reduction is significantly higher for lira compared with the other approaches, implying that the proposed model might be able to provide much more effective hedging for highly volatile currencies. The improved performance of the model can be attributed to the adjustability of the estimation horizon for the optimal hedge ratio based on the prevailing market conditions. This, in turn, allows it to better capture fat-tail properties that are frequently observed in FX returns...

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