Peter Lee

Peter Lee

United States
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Sage Arin Asset Management

About

Equity volatility relative value strategies

“Many of life's failures are people…

Activity

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Experience

  • Sage Arin Asset Management

    New York, United States

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    United States

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    United States

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    Miami, Florida, United States

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    New York, New York, United States

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Education

  • Caltech Graphic

    Caltech

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    Activities and Societies: String Theory - D-brane and holography research

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    Activities and Societies: laser/particle beam physics research, cryogenic dark matter experiment group

Publications

  • Optimal Skew Swap Replication

    As follow-up to my previous research paper, Optimal Variance Swap Replication, we propose a payoff function for realized skew swap. We then show the proposed realized skew formula can be decomposed into difference of variance and gamma swaps both of which can be replicated using vanilla options. Finally, we use the Gaussian quadrature methods of our previous work to conclude that one needs approximately eight vanilla options to closely replicate a six-month skew swap exposure for SPX.

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  • Optimal Variance Swap Replication

    We make a simple observation that variance swap replication formula is an integral of smooth function over strike space from zero to infinity and hence can be well approximated by quadrature methods. Our main insight of the paper is that Gaussian quadrature is best suited quadrature method for this problem, and the weights of the approximating summation can be interpreted as weights for strip of vanilla options that replicate the variance swap itself. For SPX, we demonstrate it requires around…

    We make a simple observation that variance swap replication formula is an integral of smooth function over strike space from zero to infinity and hence can be well approximated by quadrature methods. Our main insight of the paper is that Gaussian quadrature is best suited quadrature method for this problem, and the weights of the approximating summation can be interpreted as weights for strip of vanilla options that replicate the variance swap itself. For SPX, we demonstrate it requires around ten vanilla options to closely approximate variance swap fair value and even less number to nearly fully hedge variance swap risk exposure. We further demonstrate how to solve for optimal number of replicating vanillas by fitting a polynomial to the integrand of puts and calls. We conclude by demonstrating its effectiveness on August 5, 2024 when carry unwind triggered unprecedented volatility shock. Finally, we note that this methodology can be applied to other European style derivative contracts such as gamma swaps and conditional variance swaps.

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  • VIX1D with overnight weighting

    CBOE VIX1D suffers from intraday drift higher due to its methodology of ignoring overnight time weighting. Namely, VIX1D gaps lower between closing time and the next day open due to this effect. Empirically, the gap lower was around 20% from November 2023 to November 2024. As pointed out by [1], this is because especially when there is term structure of volatility, CBOE methodology can lead to significant bias early in the trading hours. However, this bias will go away at close, since by…

    CBOE VIX1D suffers from intraday drift higher due to its methodology of ignoring overnight time weighting. Namely, VIX1D gaps lower between closing time and the next day open due to this effect. Empirically, the gap lower was around 20% from November 2023 to November 2024. As pointed out by [1], this is because especially when there is term structure of volatility, CBOE methodology can lead to significant bias early in the trading hours. However, this bias will go away at close, since by construction, VIX1D will close at business day volatility with 252-day convention. Authors in [1] propose using forward volatility to address this issue. However, this will lead to a jump of the index across closing times as it measures forward volatility with different dates, and it does not address overnight weighting. Furthermore, it measures a different volatility than the spirit of VIX1D, which is meant to measure spot 1 day volatility. In this paper, we incorporate overnight weighting in our proposed VIX1D. This leads to continuous index even across closing times, fixes overnight bias, and furthermore allows VIX1D calculation overnight.

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  • Empirical Model of VIX Volatility and SPX Variance

    We introduce a toy model for VIX futures dynamics using the Shifted-Lognormal Model (SLN) model that does an excellent job of fitting VIX option prices with only two parameters. Then using the results of Roger Lee who studied SLN models in detail, we propose a way to extrapolate VIX volatility surface which by construction is arbitrage free. Then, we derive analytical formula for forward variance in this model and relate risks of VIX volatility surface with that of SPX volatility surface by…

    We introduce a toy model for VIX futures dynamics using the Shifted-Lognormal Model (SLN) model that does an excellent job of fitting VIX option prices with only two parameters. Then using the results of Roger Lee who studied SLN models in detail, we propose a way to extrapolate VIX volatility surface which by construction is arbitrage free. Then, we derive analytical formula for forward variance in this model and relate risks of VIX volatility surface with that of SPX volatility surface by matching variance swaps results from both markets. This allows one to relate risk parameters between VIX and SPX volatility surface, namely we derive a nonlinear equation that relates VIX skew and SPX skew. This can be used for cross market hedging, arbitrage and enhanced risk monitoring.

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  • A Note on Binomial Tree Convergence for Option Valuation

    We propose a minimal modification of the CRR model which leads to an order of magnitude improvement in rate of convergence with only around 10% more in computational overhead.

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  • Index volatility surface via moment-matching techniques

    RISK

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  • Corporate Bond Risk from Stock Dividend Uncertainty

    International Journal of Theoretical and Applied Finance

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  • Debt Subordination and the Pricing of Credit Default Swaps


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Honors & Awards

  • NSF Fellowship

    NSF

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