Derivative Securities Research Articles

The Model-Free Equivalence Condition for American Spread Options

A spread option involves the right to obtain the spread between two asset prices at a predefined strike price. This type of derivative security is frequently used in financial markets and academic finance. Furthermore, analysts use the spread option technique for real option modeling purposes. Some spread options are American-type in the sense that an option holder may exercise her option prior to the expiration. In this paper, we propose an equivalence condition for American spread options under which they are not exercised early, and are therefore equivalent to European options. Our theoretical results, developed within a model-free economic setting, suggest that the equivalence conditions documented by previous papers do not hold in a distribution-free environment. Traders, quantitative modelers, and financial programmers in various derivatives markets and the real option modeling area may use our results.

Efficient Computation of Option Prices and Greeks by Quasi--Monte Carlo Method with Smoothing and Dimension Reduction

Discontinuities and high dimensionality are common in the problems of pricing and hedging of derivative securities. Both factors have a tremendous impact on the accuracy of the quasi--Monte Carlo (QMC) method. An ideal approach to improve the QMC method is to transform the functions to make them smoother and having smaller effective dimension. This paper develops a two-step procedure to tackle the challenging problems of both the discontinuity and the high dimensionality concurrently. In the first step, we adopt the smoothing method to remove the discontinuities of the payoff function, improving the smoothness. In the second step, we propose a general dimension reduction method (called the CQR method) to reduce the effective dimension such that the better quality of QMC points in their initial dimensions can be fully exploited. The CQR method is based on the combination of the $k$-means clustering algorithm and the QR decomposition. The $k$-means clustering algorithm, a classical algorithm of machine lear...

Market completion with derivative securities

Let S^{F} be a ℙ-martingale representing the price of a primitive asset in an incomplete market framework. We present easily verifiable conditions on the model coefficients which guarantee the completeness of the market in which in addition to the primitive asset, one may also trade a derivative contract S^{B}. Both S^{F} and S^{B} are defined in terms of the solution X to a two-dimensional stochastic differential equation: S^{F}_{t} = f(X_{t}) and S^{B}_{t}:=mathbb{E}[g(X_{1}) | mathcal{F}_{t}]. From a purely mathematical point of view, we prove that every local martingale under ℙ can be represented as a stochastic integral with respect to the ℙ-martingale S :=(S^{F}, S^{B}). Notably, in contrast to recent results on the endogenous completeness of equilibria markets, our conditions allow the Jacobian matrix of (f,g) to be singular everywhere on mathbb{R}^{2}. Hence they cover as a special case the prominent example of a stochastic volatility model being completed with a European call (or put) option.

Does the Tail Wag the Dog?Evidence from Fund Flow to VIX ETFs and ETNs

Modern derivatives pricing models develop pricing relationships from the principle of no-arbitrage, assuming that if an arbitrage opportunity were to arise in the market, it would be immediately eliminated by active arbitrageurs. With this assumption, the supply curve for the derivative security is infinitely elastic at the model price, so that effects of fluctuation in supply and demand from non-arbitrageurs are suppressed. In particular, flows of funds into and out of mutual funds and ETFs should not affect market prices for the underlying securities. This article explores whether that assumption holds in the real world for ETFs based on the VIX volatility index, and finds that it doesn’t. Examining 13 volatility funds separated into four groups according to whether the focus is on nearby or longer horizons and whether volatility exposure is long or short, the authors show that fund flows respond to observed market volatility, flowing into long (short) exposure funds when the market is calm (volatile). Moreover, the VIX responds to fund flows, rising (falling) when money is flowing into long (short) exposure funds. But the evidence shows that this effect is no stronger, i.e., not unusually destabilizing, in periods of high volatility.

Optimal diversification of the securities portfolio

The article deals with problems of the theory and methods of forming the optimal portfolio of financial markets. The analytical review of methods in their historical development is given. Recommendations on the use of a particular method depends on the specific conditions are formulated. The classical and alternative methods are considered. The main attention is paid to the analysis of the investment portfolio of derivative securities in B/S-market modelThe article deals with problems of the theory and methods of forming the optimal portfolio of financial markets. The analytical review of methods in their historical development is given. Recommendations on the use of a particular method depends on the specific conditions are formulated. The classical and alternative methods are considered. The main attention is paid to the analysis of the investment portfolio of derivative securities in -market model

Hedging with small uncertainty aversion

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their “distance” to a reference local volatility model. In the limit for small uncertainty aversion, this leads to explicit formulas for prices and hedging strategies in terms of the security’s cash gamma.

Closed-form solutions for options with random initiation under asset price monitoring

This paper studies derivatives to prepare for financial risk from unexpected events. It is difficult for firms and financial institutions to hedge losses triggered by natural catastrophes such as earthquakes, by using derivative securities with fixed initiation and maturities. In this context, we consider an option that is initiated at random by an unexpected event, and moreover, is connected with a barrier of knock-in or knock-out type for asset price monitoring until the time of event. We derive closed-form valuation formulas for these options.

Valuation of American Options: Monte-Carlo Simulation and Mathematical Approximation Methods

The use of American style equity options as hedging instrument has gained currency in recent times. This phenomenon devolves from the ever-expanding need by individuals, corporations and governments to hedge away their financial risks and the clarion call for derivative securities that give the holder increased flexibility in exercise. Nevertheless, pricing American options is complex and there exists no analytic solution to the problem except a profusion of approximation and finite difference techniques. Indeed, many researchers have shown that these methods cannot handle multifactor situations where the underlying asset follows a jump-diffusion process and where the derivative security depends on multiple sources of uncertainty such as stochastic volatility, stochastic interest rate among others. Monte-Carlo simulation techniques therefore developed out of the search for a pricing formula that has the capacity to accommodate all forms of uncertainty and at the same time able to produce speedy and accurate results. Some scholars at first rejected these techniques as yielding inaccurate results but in recent times, many researchers have demonstrated the efficacy of Monte-Carlo simulation in option pricing. The aim of this study is to assess the effectiveness of Monte-Carlo simulation methods in comparison with other option pricing techniques. To achieve this objective, the research builds an algorithm to compute Call and Put prices based on a wide range of input parameters. It also develops a model where volatility or interest rate is stochastic and a deterministic function of time. The results indicate that Monte-Carlo simulation techniques produce option values and exercise boundaries that are very similar to the Binomial, Barone-Adesi and Whaley as well as the Explicit Finite Difference methods. The results also show that the stochastic volatility and stochastic interest rate models yield slightly different but more accurate results. Consequently, the study recommends simulation techniques that incorporate multiple sources of uncertainty simultaneously for fast, efficient and more accurate option pricing.

Does the Liquidity of Underlying Stocks Affect the Liquidity of Derivatives? Evidence from a Natural Experiment *

Abstract This paper documents a significant positive impact of the liquidity of underlying stocks on the liquidity of derivative securities on the basis of a sample of options and derivative warrants traded in Hong Kong. The study relies on an exogenous change in the liquidity of underlying stocks, namely, the tick size reduction implemented by the Hong Kong Stock Exchange (HKEx), which significantly reduces the bid-ask spreads of underlying stocks. The bid-ask spreads of derivative securities are also significantly reduced, especially those less liquid and with a greater inventory risk. The results of the paper are consistent with the derivative hedging theory of Cho and Engle (1999) and shed light on the sources of the liquidity of derivative securities.

Hedging derivative securities with volatility futures

We show a method to replicate S&P 500 exchange traded fund (ETF) European synthetic put by optimally rebalancing a portfolio of the underlying ETF shares, the VIX futures contracts, and treasury bonds over discrete periods. The motivation for this study is two-fold. Firstly, market-makers in S&P 500 index options may need to hedge a large short position synthetically when the puts are in short supply. Secondly, for an institutional investor holding a large diversified portfolio of US stocks, constructing a long position in synthetic puts is tantamount to providing portfolio insurance. The put replication is useful as the alternative of buying US puts can be prohibitively expensive in a distressed market. The numerical method of Gauss-Hermite quadrature is employed in the optimal solution. Both simulations and empirical validation using historical S&P 500 index ETF and VIX futures price data show effectiveness in the put pricing versus more traditional methods.

Hedging derivative securities with volatility futures

We show a method to replicate S&P 500 exchange traded fund (ETF) European synthetic put by optimally rebalancing a portfolio of the underlying ETF shares, the VIX futures contracts, and treasury bonds over discrete periods. The motivation for this study is two-fold. Firstly, market-makers in S&P 500 index options may need to hedge a large short position synthetically when the puts are in short supply. Secondly, for an institutional investor holding a large diversified portfolio of US stocks, constructing a long position in synthetic puts is tantamount to providing portfolio insurance. The put replication is useful as the alternative of buying US puts can be prohibitively expensive in a distressed market. The numerical method of Gauss-Hermite quadrature is employed in the optimal solution. Both simulations and empirical validation using historical S&P 500 index ETF and VIX futures price data show effectiveness in the put pricing versus more traditional methods.

The Trader’s Voice: Rick Santelli’s Tea Party Rant

This essay explores the micro-origins of the Tea Party movement, focusing on Rick Santelli’s February 2009 ‘rant’ at the Chicago Mercantile Exchange. Contrary to populist readings of the movement and its later anti-Obamacare positions, a close reading of the rhetorical and media contexts of the rant demonstrates that its origins lay in a defense of unregulated, untaxed derivative securities. The particular configuration of the HDTV image and viralizable video content contributed to both the power of the rant and the erasure of its particular context.

Real-Time Risk Management: An AAD-PDE Approach

We apply adjoint algorithmic differentiation (AAD) to the risk management of derivative securities in the situation where the dynamics of securities prices are given in terms of partial differential equations (PDE). With simple examples, we show how AAD can be applied to both forward and backward PDEs in a straightforward manner. In particular, in the context of one-factor short-rate models for interest rates or default intensity processes, we show how one can compute price sensitivities reliably and orders of magnitude faster than with a standard finite-difference approach. This significantly increased efficiency is obtained by combining (i) the adjoint of a forward PDE for calibrating the parameters of the model, (ii) the adjoint of a backward PDE for pricing the derivative security, and (iii) the implicit function theorem to avoid iterating the calibration procedure.

Numerical valuation of derivatives in high-dimensional settings via partial differential equation expansions

We propose a new numerical approach to solving high-dimensional partial differential equations (PDEs) that arise in the valuation of exotic derivative securities. The proposed method is extended from the work of Reisinger andWittum and uses principal component analysis of the underlying process in combination with a Taylor expansion of the value function into solutions to low-dimensional PDEs. The approximation is related to anchored-analysis-of-variance decompositions and is expected to be accurate whenever the covariance matrix has one or few dominating eigenvalues. We give a careful analysis of the numerical accuracy and computational complexity compared with state-of-the-art Monte Carlo methods, using Bermudan swaptions and ratchet floors, which are considered difficult benchmark problems, as examples. We demonstrate that, for problems with medium to high dimensionality and moderate time horizons, the PDE method presented delivers results comparable in accuracy to the Monte Carlo methods considered here in a similar or (often significantly) faster run time.

How Do Turkish Mutual Funds and Investment Trusts Use Derivative Instruments?

This paper centers on the question of how derivative securities are actually used by investment managers. In this vein, we analyze the use of derivatives by mutual funds and investment trusts by comparing three characteristics of funds that use derivatives and that do not. For the years 2008 and 2009, we examine totally 193 funds and our first classification is “investment objectives” and our results show that the 43.40% (22.12%) [51.85%] of the funds invested in only equity (bonds) [balanced as equity and bonds] use derivatives. Secondly, in terms of their “legal structures” and we find that 56.67% of the closed-ended and 27.61% of the open-ended funds use derivatives. As a final classification called as “fund-type”, it is observed that 51.89% (8.03%) of the A-type (B-type) fund investors use derivatives. We proceed with logit analysis to identify the relation between characteristics of funds and derivative usage. We find for all the classification of funds that the likelihood of derivative usage increases as the turnover of funds escalates. Furthermore, we make univariate analyses to compare distributional parameters between users and non-users. In terms of the “investment objectives”, derivative users having bond dominated portfolios have higher standard deviation, idiosyncratic risk and skewness, while those of non-users have higher beta and timing beta. For the structural classification, users significantly have higher standard deviation, idiosyncratic risk and skewness and yet non-users have a higher beta and timing beta. In case of the fund type, non-users have a higher beta yet a lower kurtosis. Lastly, we apply regression analyses to test relation between the change in the risk variables between the first six months of the year, and fund/trust performance during the first six months of the year. The empirical results indicate that the negative relationship between past performance and change in risk is weaker for derivative user funds/trusts.

Model-Free Methods in Valuation and Hedging of Derivative Securities

Were “the quants” to blame for the financial crisis of 2008? In narrow terms the answer appears to be “no” on the argument put forward by Alex Lipton, that the banks that survived were using the same models as those that failed. Be that as it may, it does seem that a contributory factor in the crisis was over-reliance on models that, in retrospect, had insufficient credibility.

Hedging Price Risk in the Presence of Quantity Risk

This research looks into hedge strategies to resolve foreign exchange-related risks, generated when investing in overseas financial assets, as an example of quantity risk. If an investor has information with no uncertainty over the volume and there is only a price risk he want to hedge, an investor will be able to reduce or eliminate risks by using relative derivative securities such as forwards or futures contracts. However, if there are uncertainties over the volume of hedging targets that is called quantity risk, it is impossible to set the optimal hedge ratio with the traditional method without considering the presence of quantity risk. In this paper, we theoretically draw an optimal hedge ratio which is estimated via minimal variance criterion under static hedge structure. We also analyze its hedge performance and the impact of change in covariance on the optimal hedge ratio and variance of investment return denominated as its own country currency. For theoretical approach, we review the impact that overseas financial assets’ yield and exchanges rates distribution will have on optimal hedge ratio through simple numerical analysis. Empirical analysis is carried out by using the stock indices of the U.S., Europe and Asian countries, and the results indicate that hedge strategies taken with quantity risk for all markets produced better hedging performance than the strategies taken without quantity risk. Since there is a need for systematic research on risks involving foreign exchanges that occur in the event of foreign investments aimed to develop the domestic financial industry, we hope that our research serve as a stepping-stone for further research.

Optimal limit methods for computing sensitivities of discontinuous integrals including triggerable derivative securities

We introduce an approach to computing sensitivities of discontinuous integrals. The methodology is generic in that it only requires knowledge of the simulation scheme and the location of the integrand’s singularities. The methodology is proven to be optimal in terms of minimizing the variance of the measure changes. For piecewise constant payoffs this minimizes the variance of Monte Carlo sensitivities. An efficient adjoint implementation is discussed, and the method is shown to be effective for a number of natural financial examples including double barrier options and triggerable interest rate derivative securities.

Credit risk and contagion via self-exciting default intensity

Recent empirical evidences indicate that default rates are influenced not only by the observable or latent risk factors, but also depend on the history of past defaults. Motivated by this empirical finding, we consider in this paper a reduced-form, intensity-based credit risk model, which allows for both frailty and default contagion, using a so-called “self-exciting” intensity, in the sense that the default intensity varies not only with the risk factors, but also depends on the previous default history of all the firms. With “self-exciting” default intensity, we are able to obtain closed-form expressions for the pricing of credit derivative securities in our model. The estimation of parameters using the EM algorithm is considered as well.

INVESTASI SEKURITAS DERIVATIF DI PASAR MODAL INDONESIA

The world will never forget about the big shock in capital market in America “Black October event” or Black Tuesday that occurred in 1929 and known as The Great Depression that cause fall in world economy. However, there is always have a wisdom behind an event, that is the birth of a new investment product called derivative instrument. The derivative instrument is a financial instrument that constitute derivative asset from the underlying asset, both derived from stocks and bonds. There are There are several kinds of derivative securities which warrant, right, option, forward, futures, and swap. In Indonesia, although it is still new, investment od derivative instrumen looks like the “fresh wind” for investor amid tight and hard competition finance business. The proof, many big companies are investing in derivative securities such as, Quaker Oats were issued Future, Indosat Warrant issued, as well as issuing the Right of Niaga Bank.