Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee-Carter Framework

Longevity risk is a major issue for insurers and pension funds, especially in the selling of annuity products. In that respect, securitization of this risk could offer great opportunities for hedging. This article proposes to design survivor bonds which could be issued directly by insurers. In order to guaranty some transparency in the product, the survivor bond is based on a public mortality index. The classical Lee‐Carter model for mortality forecasting is used to price a risky coupon survivor bond based on this index.     

A new approach for option pricing under stochastic volatility

We develop a new approach for pricing European-style contingent claims written on the time T spot price of an underlying asset whose volatility is stochastic. Like most of the stochastic volatility literature, we assume continuous dynamics for the price of the underlying asset. In contrast to most of the stochastic volatility literature, we do not directly model the dynamics of the instantaneous volatility. Instead, taking advantage of the recent rise of the variance swap market, we directly assume continuous dynamics for the time T variance swap rate. The initial value of this variance swap rate can either be directly observed, or inferred from option prices. We make no assumption concerning the real world drift of this process. We assume that the ratio of the volatility of the variance swap rate to the instantaneous volatility of the underlying asset just depends on the variance swap rate and on the variance swap maturity. Since this ratio is assumed to be independent of calendar time, we term this key assumption the stationary volatility ratio hypothesis (SVRH). The instantaneous volatility of the futures follows an unspecified stochastic process, so both the underlying futures price and the variance swap rate have unspecified stochastic volatility. Despite this, we show that the payoff to a path-independent contingent claim can be perfectly replicated by dynamic trading in futures contracts and variance swaps of the same maturity. As a result, the contingent claim is uniquely valued relative to its underlying’s futures price and the assumed observable variance swap rate. In contrast to standard models of stochastic volatility, our approach does not require specifying the market price of volatility risk or observing the initial level of instantaneous volatility. As a consequence of our SVRH, the partial differential equation (PDE) governing the arbitrage-free value of the contingent claim just depends on two state variables rather than the usual three. We then focus on the consistency of our SVRH with the standard assumption that the risk-neutral process for the instantaneous variance is a diffusion whose coefficients are independent of the variance swap maturity. We show that the combination of this maturity independent diffusion hypothesis (MIDH) and our SVRH implies a very special form of the risk-neutral diffusion process for the instantaneous variance. Fortunately, this process is tractable, well-behaved, and enjoys empirical support. Finally, we show that our model can also be used to robustly price and hedge volatility derivatives.     

Securitization of Longevity Risk Using Percentile Tranching

Securitizations that transfer risk to the financial markets are a potential solution to longevity risk in the annuity business. The classical Lee–Carter model is applied to generate the future stochastic survival distribution. A method to design inverse survivor bonds using percentile tranches and to calculate the security prices is presented. The percentile tranche method is a simple and practical way for the issuer to design and price the security. This method can serve to identify the risk–yield relationship, which can provide investors with clear insight regarding the appropriate choice of tranches.     

Pricing default swaps: Empirical evidence

In this paper we compare market prices of credit default swaps with model prices. We show that a simple reduced form model outperforms directly comparing bonds' credit spreads to default swap premiums. We find that the model yields unbiased premium estimates for default swaps on investment grade issuers, but only if we use swap or repo rates as proxy for default-free interest rates. This indicates that the government curve is no longer seen as the reference default-free curve. We also show that the model is relatively insensitive to the value of the assumed recovery rate.     

THE PROPOSED INTRODUCTION OF FUTURES‐STYLE MARGINING IN THE UNITED STATES: AN AUSTRALIAN COMPARISON

We extend the quadratic approximation method to examine American‐style options traded using futures‐style margining and show that an early exercise premium can exist when the cost of carry is negative. Empirical results based on a reduced form of the model using futures‐style call options traded on the Australian All Ordinaries Share Price Index are consistent with previous research: call option early exercise premiums are economically zero. Full option prices are examined by comparing observed futures‐style with theoretical stock‐style values. We find futures‐style values exceed stock‐style values and argue that the increase results from improvements in liquidity. The findings are particularly relevant given the pending decision at the Commodity Futures Trading Commission to introduce a futures‐style system in the United States. JEL classification: G13, C13     

An analysis of option pricing under systematic consumption risk using GARCH

An issue in the pricing of contingent claims is whether to account for consumption risk. This is relevant for contingent claims on stock indices, such as the FTSE 100 share price index, as investor’s desire for smooth consumption is often used to explain risk premiums on stock market portfolios, but is not used to explain risk premiums on contingent claims themselves. This paper addresses this fundamental question by allowing for consumption in an economy to be correlated with returns. Daily data on the FTSE 100 share price index are used to compare three option pricing models: the Black–Scholes option pricing model, a GARCH (1, 1) model priced under a risk-neutral framework, and a GARCH (1, 1) model priced under systematic consumption risk. The findings are that accounting for systematic consumption risk only provides improved accuracy for in-the-money call options. When the correlation between consumption and returns increases, the model that accounts for consumption risk will produce lower call option prices than observed prices for in-the-money call options. These results combined imply that the potential consumption-related premium in the market for contingent claims is constant in the case of FTSE 100 index options.     

Convergent synergies in the global market for corporate control

We investigate the informational role of the takeover premium as a forward looking price to expected synergies in the global market for corporate control. We find that premiums paid in the global market for corporate control are clustered in waves and driven to some extent by the US premium. International takeover premiums have become more responsive to US premiums as the globalization process evolved over time. Short-run divergent dynamics due to idiosyncratic or country-specific factors have become less severe, which suggests that expected synergies have become increasingly integrated in the global market for corporate control. Furthermore, we find that the region’s takeover premiums typically become more responsive to US takeover premiums when US economic conditions are relatively weak, when the US monetary policy is restrictive, when US credit risk is high, and when the region’s corporate governance (as measured by legal system quality and accounting quality) is high.     

Survivor Swaps

A survivor swap (SS) is an agreement to exchange cash flows in the future based on the outcome of at least one survivor index. This article discusses the possible uses of SSs as instruments for managing, hedging, and trading mortality‐dependent risks. SSs are especially useful for insurance companies, but also offer other interested parties low beta avenues into the acquisition of mortality risk exposure. The article also investigates vanilla SSs in some detail, and suggests how their premiums and values might be determined in an incomplete market setting.     

An alternative approach to the valuation of American options and applications

In this paper we examine the structure of American option valuation problems and derive the analytic valuation formulas under general underlying security price processes by an alternative but intuitive method. For alternative diffusion processes, we derive closed-form analytic valuation formulas and analyze the implications of asset price dynamics on the early exercise premiums of American options. In this regard, we introduce useful and interesting diffusion processes into American option-pricing literature, thus providing a wide range of choices of pricing models for various American-type derivative assets. This work offers a useful analytic framework for empirical testing and practical applications such as the valuation of corporate securities and examining the impact of options trading on market micro-structure.     

A bivariate model for evaluating equity-linked policies with surrender option

This article proposes a bivariate lattice model for evaluating equity-linked policies embedding a surrender option when the underlying equity dynamics is described by a geometric Brownian motion with stochastic interest rate. The main advantage of the model stays in that the original processes for the reference fund and the interest rate are directly discretized by means of lattice approximations, without resorting to any additional transformation. Then, the arising lattices are combined in order to establish a bivariate tree where equity-linked policy premiums are computed by discounting the policy payoff over the lattice branches, and allowing early exercise at each premium payment date to model the surrender decision.     

The market premium for the option to close: evidence from Australian gold mining firms

This study shows the market value of gold mining firms contains a premium for the option to close. The sample uses 41 gold mining producers listed on the Australian Stock Exchange from 1987 to 2013. The premium of the market price over the present value of cash flows is isolated and a pooled cross‐sectional regression tests the degree of association between that premium and theoretical option premiums. The results show market prices incorporate a premium reflecting the option to temporarily close operations. The magnitude of the option premium to close depends on whether firms are out or in the money options.     

Optimal Refunding Strategies, Transaction Costs, and the Market Value of Corporate Debt

The primary purpose of this paper is to consider both qualitatively and quantitatively the effects of refunding transaction costs and interest rate uncertainty on optimal refunding strategies and the market value of corporate debt. A dynamic model of corporate bond refunding with transaction costs is developed that simultaneously solves for the optimal refunding strategy, the value of the refunding call option, the value of the bond liability to the firm, and the market (investor) value of the fixed-rate contract. We provide examples in which the price of the callable bond does exceed the call price, and we examine whether or not typical levels of refunding costs are sufficient to explain the magnitude and duration of frequently observed premiums on callable corporate bonds.     

Pricing Property Index Linked Swaps with Counterparty Default Risk

This paper extends Bjork and Clapham (Journal of Housing Economics 11:418–432, 2002) model for pricing real estate index total return swaps. Our extension considers counterparty default risk within a first passage contingent claims model. We price total return swaps on property indices with different levels of default risk. We develop this model under same assumptions as Bjork and Clapham (Journal of Housing Economics 11:418–432, 2002) and find that total return swap price is no longer zero. Total return swap payer must charge a spread over the market interest rate that compensates him for the exposure to this additional risk. Based on commercial property indices in the UK, we observe that computed spreads are much lower than a sample of quotes obtained from one of the traders in the market.     

Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index

In this paper a couple of variance dependent instruments in the financial market are studied. Firstly, a number of aspects of the variance swap in connection to the Barndorff-Nielsen and Shephard model are studied. A partial integro-differential equation that describes the dynamics of the arbitrage-free price of the variance swap is formulated. Under appropriate assumptions for the first four cumulants of the driving subordinator, a Ve?e?-type theorem is proved. The bounds of the arbitrage-free variance swap price are also found. Finally, a price-weighted index modulated by market variance is introduced. The large-basket limit dynamics of the price index and the “error term” are derived. Empirical data driven numerical examples are provided in support of the proposed price index.     

Estimating Early Exercise Premiums on Gold and Copper Options Using a Multifactor Model and Density Matched Lattices

We use the standard geometric Brownian motion augmented by jumps to describe the spot underlying and mean regressive models of interest rates and convenience yields as state variables for gold and copper prices. Estimates of parameters of the diffusion processes are obtained by the Kalman filter. Using these estimates, jump parameters are estimated in the second stage by least squares. Early exercise premia on puts and calls are computed using a lattice with probabilities assigned by the density matching technique. We find that while deep in the money options have greater absolute early exercise premiums, the early exercise premium is roughly constant as a percent of option price. Our findings also confirm that gold behaves like an investment asset and copper behaves like a commodity.     

Accounting for Option–based Compensation: The Economic Cost Approach

The intrinsic value approach amortizes over the life of the option, the difference between the stock price on the date of the grant and the exercise price of the option. The fair market value approach amortizes over the life of the option, the market value of stock options on the date of the grant. These approaches do not reflect the changes in the option–based compensation cost after the grant date. This paper proposes an economic cost approach that not only adjusts for the changes in the value of the options during its life but also records the issuance of the stock at fair market value on the exercise date.     

The dynamics of sovereign yields over swap rates in the Eurozone market

We explore the dynamics of the adjusted swap spread (calculated as the difference between the swap rate and sovereign yields over the credit default swap premium) in the Eurozone market by studying three markets simultaneously: 1) sovereign bonds, 2) credit default swaps (CDS), and 3) swap rates. We find a strong relationship between the markets. Specifically, based on the no-arbitrage argument, we show that the difference between the Euribor and Repo rates is a key driver of the adjusted swap spread. However, illiquidity premiums and systemic risk also play an essential role in times of economic stress and for less creditworthy countries. The findings also shed light on the recent negative swap spreads puzzle in the United States.     

Optimal investment and contingent claim valuation in illiquid markets

This paper extends basic results on arbitrage bounds and attainable claims to illiquid markets and general swap contracts where both claims and premiums may have multiple payout dates. Explicit consideration of swap contracts is essential in illiquid markets where the valuation of swaps cannot be reduced to the valuation of cumulative claims at maturity. We establish the existence of optimal trading strategies and the lower semicontinuity of the optimal value of optimal investment under conditions that extend the no-arbitrage condition in the classical linear market model. All results are derived with the “direct method” without resorting to duality arguments.     

客户规模与审计费用溢价的研究:来自2001—2004年沪市的初步证据

本文以2001—2004年我国沪市上市公司为研究对象,利用修正的Simunic模型对不同资产规模的客户支付给"五大"的费用溢价进行研究。结果表明:大型客户向国内"五大"支付审计费用溢价,而小客户则不支付溢价。这与早先Francis和Stokes提出的论断不相符合,说明中国审计市场的内在运行机理可能在某些方面异于海外市场,这可能是因为在两种不同的经济体中,"五大"的市场地位、战略以及上市公司的需求各不相同所导致的。     

LIBOR and swap market models and measures

A self-contained theory is presented for pricing and hedging LIBOR and swap derivatives by arbitrage. Appropriate payoff homogeneity and measurability conditions are identified which guarantee that a given payoff can be attained by a self-financing trading strategy. LIBOR and swap derivatives satisfy this condition, implying they can be priced and hedged with a finite number of zero-coupon bonds, even when there is no instantaneous saving bond. Notion of locally arbitrage-free price system is introduced and equivalent criteria established. Stochastic differential equations are derived for term structures of forward libor and swap rates, and shown to have a unique positive solution when the percentage volatility function is bounded, implying existence of an arbitrage-free model with such volatility specification. The construction is explicit for the lognormal LIBOR and swap “market models”, the former following Musiela and Rutkowski (1995). Primary examples of LIBOR and swap derivatives are discussed and appropriate practical models suggested for each.