Pricing American Options on Leveraged Exchange Traded Funds in the Binomial Pricing Model

This paper describes our work pricing options in the binomial model on leveraged exchange traded funds (ETFs) with three different approaches. A leveraged exchange traded fund attempts to achieve a similar daily return as the index it follows but at a specified positive or negative multiple of the return of the index. We price options on these funds using the leveraged multiple, predetermined by the leveraged ETF, of the volatility of the index. The initial approach is a basic time step approach followed by the standard Cox, Ross, and Rubinstein method. The final approach follows a different format which we will call the Trigeorgis pricing model. We demonstrate the difficulties in pricing these options based off the dynamics of the indices the ETFs follow

Price Dynamics & Trading Strategies in the Commodities Market

This thesis makes new observations of market phenomena for various commodities and trading strategies centered around these observations. In particular, our results imply that many aspects of the commodities markets, from delivery markets to producers and consumer derivative based ETFs can be modeled eectively using nancial engineering techniques. Chapter 2 examines what drives the returns of gold miner stocks and ETFs. Inspired by our real options model, we construct a method to dynamically replicate gold miner stocks using two factors: a spot gold ETF and a market equity portfolio. We find that our real options approach can explain a significant portion of the drivers of firm implied gold leverage. Chapter 3 studies commodity exchange-traded funds (ETFs). From empirical data, we find that many commodity leveraged ETFs underperform significantly against our constructed dynamic benchmark, and we quantify such a discrepancy via the novel idea of realized effective fee. Finally, we consider a number of trading strategies and examine their performance by backtesting with historical price data. Chapter 4 studies the phenomenon of non-convergence between futures and spot prices in the grains market. In our proposed approach, we incorporate stochastic spot price and storage cost, and solve an optimal double stopping problem to understand shipping certificate prices. Our new models for stochastic storage rates explain the spot-futures premium

LEVERAGED ETF IMPLIED VOLATILITIES FROM ETF DYNAMICS

The growth of the exchange-traded fund (ETF) industry has given rise to the trading of options written on ETFs and their leveraged counterparts (LETFs). We study the relationship between the ETF and LETF implied volatility surfaces when the underlying ETF is modeled by a general class of local-stochastic volatility models. A closed-form approximation for prices is derived for European-style options whose payoffs depend on the terminal value of the ETF and/or LETF. Rigorous error bounds for this pricing approximation are established. A closed-form approximation for implied volatilities is also derived. We also discuss a scaling procedure for comparing implied volatilities across leverage ratios. The implied volatility expansions and scalings are tested in three settings: Heston, limited constant elasticity of variance (CEV), and limited SABR; the last two are regularized versions of the well-known CEV and SABR models

Compare the out-of-sample performance of mean-variance optimization relative to equally weighted or naîve 1/N portfolio

Masteroppgave i finansiering og investering - Nord universitet 202

Essays in Financial Engineering

This thesis consists of three essays in financial engineering. In particular we study problems in option pricing, stochastic control and risk management. In the first essay, we develop an accurate and efficient pricing approach for options on leveraged ETFs (LETFs). Our approach allows us to price these options quickly and in a manner that is consistent with the underlying ETF price dynamics. The numerical results also demonstrate that LETF option prices have model-dependency particularly in high-volatility environments. In the second essay, we extend a linear programming (LP) technique for approximately solving high-dimensional control problems in a diffusion setting. The original LP technique applies to finite horizon problems with an exponentially-distributed horizon, T. We extend the approach to fixed horizon problems. We then apply these techniques to dynamic portfolio optimization problems and evaluate their performance using convex duality methods. The numerical results suggest that the LP approach is a very promising one for tackling high-dimensional control problems. In the final essay, we propose a factor model-based approach for performing scenario analysis in a risk management context. We argue that our approach addresses some important drawbacks to a standard scenario analysis and, in a preliminary numerical investigation with option portfolios, we show that it produces superior results as well

Essays in financial economics

In the first paper of my dissertation I study the size and source of exchange-traded funds’ (ETFs) price impact in the most ETF-dominated asset classes: volatility (VIX) and commodities. I show that the introduction of ETFs increased futures prices. To identify ETF-induced price distortions, I propose a model-independent approach to replicate the value of a VIX futures contract. This allows me to isolate a nonfundamental component in VIX futures prices, of 18.5% per year, that is strongly related to the rebalancing of ETFs. To understand the source of that component, I decompose trading demand from ETFs into three main parts: leverage rebalancing, calendar rebalancing, and flow rebalancing. Leverage rebalancing has the largest effects. It amplifies price changes and introduces unhedgeable risks for ETF counterparties. Surprisingly, providing liquidity to leveraged ETFs turns out to be a bet on variance, even in a market with a zero net share of ETFs. Trading against leverage rebalancing delivers large abnormal returns and Sharpe ratios above two across markets. The second paper analyses the impact of the ECB’s Corporate Sector Purchase Programme (CSPP) announcement on prices, liquidity and debt issuance in the European corporate bond market. I find that the quantitative easing (QE) programme increased prices and liquidity of bonds eligible to be purchased substantially. Bond yields dropped on average by 30 bps (8%) after the CSPP announcement. Tri-party repo turnover rose by 8.15 million USD (29%), and bilateral turnover went up by 7.05 million USD (72%). Bid-ask spreads also showed significant liquidity improvement in eligible bonds. QE was successful in boosting corporate debt issuance. Firms issued 2.19 billion EUR (25%) more in QE-eligible debt after the CSPP announcement, compared to other types of debt. Surprisingly, corporates used the attracted funds mostly to increase dividends. These effects were more pronounced for longer-maturity, lower-rated bonds, and for more credit-constrained, lower-rated firms. The third paper (co-authored with Christian Julliard, Zijun Liu, Seyed E. Seyedan and Kathy Yuan) studies the determinants of repo haircuts in the UK market. We find that transaction maturity and collateral quality have first order importance. We also document that counterparties matter in determining haircuts. Hedge funds, as borrowers, receive significantly higher haircuts. Larger borrowers with higher ratings receive lower haircuts, but we find that these effects can be overshadowed by collateral quality. Repeated bilateral relationships also matter and generate lower haircuts. We find evidence supporting an adverse selection explanation of haircuts, but limited evidence in favor of lenders’ liquidity position or default probabilities affecting haircuts