Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models

This paper demonstrates how to value American interest rate options under the jump-extended constant-elasticity-of-variance (CEV) models. We consider both exponential jumps (see Duffie et al., 2000) and lognormal jumps (see Johannes, 2004) in the short rate process. We show how to superimpose recombining multinomial jump trees on the diffusion trees, creating mixed jump-diffusion trees for the CEV models of short rate extended with exponential and lognormal jumps. Our simulations for the special case of jump-extended Cox, Ingersoll, and Ross (CIR) square root model show a significant computational advantage over the Longstaff and Schwartz’s (2001) least-squares regression method (LSM) for pricing American options on zero-coupon bonds.     

The delivery option in credit default swaps

Under standard assumptions the reduced-form credit risk model is not capable of accurately pricing the two fundamental credit risk instruments – bonds and credit default swaps (CDS) – simultaneously. Using a data set of euro-denominated corporate bonds and CDS our paper quantifies this mispricing by calibrating such a model to bond data, and subsequently using it to price CDS, resulting in model CDS spreads up to 50% lower on average than observed in the market. An extended model is presented which includes the delivery option implicit in CDS contracts emerging since a basket of bonds is deliverable in default. By using a constant recovery rate standard models assume equal recoveries for all bonds and hence zero value for the delivery option. Contradicting this common assumption, case studies of Chapter 11 filings presented in the paper show that corporate bonds do not necessarily trade at equal levels following default. Our extension models the implied expected recovery rate of the cheapest-to-deliver bond and, applied to data, largely eliminates the mispricing. Calibrated recovery values lie between 8% and 47% for different obligors, exhibiting strong variation among rating classes and industries. A cross-sectional analysis reveals that the implied recovery parameter depends on proxies for the delivery option, primarily the number of available bonds and bond pricing errors. No evidence is found for a direct influence of the bid-ask spread, notional amount, coupon, or rating used as proxies for bond market liquidity.     

An FFT-network for Lévy option pricing

This paper develops a simple network approach to American exotic option valuation under Lévy processes using the fast Fourier transform (FFT). The forward shooting grid (FSG) technique of the lattice approach is then generalized to expand the FFT-network to accommodate path-dependent variables. This network pricing approach is applicable to all Lévy processes for which the characteristic function is readily available. In other words, the log-value of the underlying asset can follow finite-activity or infinite-activity Lévy processes. With the powerful computation of FFT, the proposed network has a negligible additional computational burden compared to the binomial tree approach. The early exercise policy and option values in the continuation region are determined in a way very similar to that of the lattice approach. Numerical examples using American-style barrier, lookback, and Asian options demonstrate that the FFT-network is accurate and efficient.     

Factorization of European and American option prices under complete and incomplete markets

In a standard option-pricing model, with continuous-trading and diffusion processes, this paper shows that the price of one European-style option can be factorized into two intuitive components: One robust, X₀, which is priced by arbitrage, and a second, Π₀, which depends on a risk orthogonal to the traded securities. This result implies the following: (1) In an incomplete market, these parts represent the price of a hedging portfolio, which is unique, and a premium, which depends only on the risk premiums associated with the residual risk, respectively. (2) In a complete market, it allows factoring the contribution of the different sources of risk to the final option price. For example, in a stochastic volatility model, we can quantify the impact on the option price of volatility risk relative to market risk, Π₀ and X₀, respectively. Hence, certain misspricings in option markets can be directly related to the premium, Π₀. (3) Moreover, these results extend to American securities, which have a third component – an additional early-exercise premium.     

Preferred habitat for liquidity in international short-term interest rates

Risk-shifting window dressing and a preferred habitat for liquidity have been offered as possible explanations as to why US money market rates are higher before the year-end than afterwards. The two hypotheses differ in the timing of the rate decline at the year-end and the evidence on the timing of the decline supports the preferred habitat hypothesis in US money markets. This paper extends this line of research to the behavior of international short-term interest rates at year-ends and quarter-ends using London interbank offer rates (LIBOR) for 11 different currencies. The results suggest that the behavior of LIBOR for five currencies: the US Dollar, Euro, Japanese Yen, Swiss Franc, and German Mark is consistent with year-end or quarter-end preferred habitats for liquidity. Other currencies do not demonstrate consistently distinct patterns in turn-of-the-year and turn-of-the-quarter yields. None of the results provides any support for risk-shifting window dressing.     

The effect of macroeconomic news on beliefs and preferences: Evidence from the options market

We examine the effect of regularly scheduled macroeconomic announcements on the beliefs and preferences of participants in the U.S. Treasury market by comparing the option-implied state-price densities (SPDs) of bond prices shortly before and after the announcements. We find that the announcements reduce the uncertainty implicit in the second moment of the SPD regardless of the content of the news. The changes in the higher-order moments, in contrast, depend on whether the news is good or bad for economic prospects. We explore three alternative explanations for our empirical findings: relative mispricing, changes in beliefs, and changes in preferences. We find that our results are consistent with time-varying risk aversion.     

Covered interest rate parity in emerging markets

This paper finds that while covered interest rate parity holds for large and small triple A rated economies, it holds for emerging markets only for a three-month maturity. For a five-year horizon the size and frequency of violations lead to the conclusion that covered interest rate parity does not hold for longer maturities for Brazil, Chile, Russia and South Korea. Overall this paper finds that aspects of credit risk are the source of violations in CIRP in the long-term capital markets rather than transactions costs or the size of the economy.     

The cross-sectional relation between conditional heteroskedasticity,the implied volatility smile,and the variance risk premium

This paper estimates how the shape of the implied volatility smile and the size of the variance risk premium relate to parameters of GARCH-type time-series models measuring how conditional volatility responds to return shocks. Markets in which return shocks lead to large increases in conditional volatility tend to have larger variance risk premia than markets in which the impact on conditional volatility is slight. Markets in which negative (positive) return shocks lead to larger increases in future volatility than positive (negative) return shocks tend to have downward (upward) sloping implied volatility smiles. Also, differences in how volatility responds to return shocks as measured by GARCH-type models explain much, but not all, of the variations in excess kurtosis and multi-period skewness across different markets.     

Order imbalance,market returns and macroeconomic news: Evidence from the Australian interest rate futures market

The relationship between order imbalance, market returns and macroeconomic news is examined in the context of the Australian interest rate futures market. Contemporaneous order imbalance exerts a significant impact on market returns in the expected direction i.e. excess buy (sell) orders drive up (down) prices. Order imbalances are related to past market returns with market participants acting in a contrarian manner across all products following market rallies. Nine major macroeconomic announcements are identified with order imbalance, and returns, reacting to such announcements in a manner that correctly reflects the news component. Following a scheduled macroeconomic announcement there is an increase in the level of information asymmetry within the interest rate futures market, demonstrated by an increased sensitivity to order flow. Finally, the pattern of order imbalance immediately prior to scheduled announcements suggests that there is no information leakage.     

An economic capital model integrating credit and interest rate risk in the banking book

Banks often measure credit and interest rate risk in the banking book separately and then add the risk measures to determine economic capital. This approach misses complex interactions between the two risk types. We develop a framework where these risks are analysed jointly. Since banking book positions are generally not marked to market, our model is based on book value accounting. Our simulations show that interactions matter, and that ignoring them leads to risk overstatement. The magnitude of the errors depends on the structure of the balance sheet and on the repricing characteristics of assets and liabilities.     

Regime dependent determinants of credit default swap spreads

Credit default swap (CDS) spreads display pronounced regime specific behaviour. A Markov switching model of the determinants of changes in the iTraxx Europe indices demonstrates that they are extremely sensitive to stock volatility during periods of CDS market turbulence. But in ordinary market circumstances CDS spreads are more sensitive to stock returns than they are to stock volatility. Equity hedge ratios are three or four times larger during the turbulent period, which explains why previous research on single-regime models finds stock positions to be ineffective hedges for default swaps. Interest rate movements do not affect the financial sector iTraxx indices and they only have a significant effect on the other indices when the spreads are not excessively volatile. Raising interest rates may decrease the probability of credit spreads entering a volatile period.     

A generalization of reset options pricing formulae with stochastic interest rates

A generalization of reset call options with predetermined dates is derived in the case of time-dependent volatility and time-dependent interest rate by applying martingale method and change of nume?aire or change of probability measure. An analytical pricing formula for the reset call option is also obtained when the interest rate follows an extended Vasicek’s model. Numerical results show that the correlated coefficient between the stock price and interest rate is almost unacted on the price of reset call option with short maturity and Monte Carlo method is inefficient. Monte Carlo method should be only used if there is no closed-formed solution for option pricing.     

The volatility of consumption-based stochastic discount factors and economic cycles

This paper aims to assess the macroeconomic and financial impact of economic uncertainty using information contained in the second moments of financial risk factors employed in the asset pricing literature. Specifically, we propose the volatility of consumption-based stochastic discount factors (SDFs) as a predictor of future economic and stock market cycles. We employ both contemporaneous and ultimate consumption risk specifications with durable and non-durable consumption. Alternative empirical tests show that this volatility has significant forecasting ability from 1985 to 2006. The degree of predictability tends to dominate that shown by standard predictor variables. We argue that the significant predictability of the volatility of consumption-based SDFs reported in this paper relies mainly on the joint effect of their components.     

Regime switches in exchange rate volatility and uncovered interest parity

We use a regime-switching model to examine how exchange rate volatility is related to the failure of uncovered interest parity. Main findings are as follows. First, exchange rate returns are strongly influenced by regime switches in the relationship between the returns and interest rate differentials. Second, low-yielding currencies appreciate less frequently, but once it occurs, their movements are faster than when they depreciate. Third, depreciation of low-yielding currencies and low volatility are mutually dependent on each other. Finally, these three findings are more evident for shorter horizons. The second and third results are consistent with a market participants’ view: short-term carry trades in a low-volatility environment and their rapid unwinding substantially influence exchange rates. We consider the effects of funding liquidity to explain these results.     

Expected returns, risk premia, and volatility surfaces implicit in option market prices

This article presents a pure exchange economy that extends Rubinstein (1976) to show how the jump-diffusion option pricing model of Merton (1976) is altered when jumps are correlated with diffusive risks. A non-zero correlation between jumps and diffusive risks is necessary in order to resolve the positively sloped implied volatility term structure inherent in traditional jump diffusion models. Our evidence is consistent with a negative covariance, producing a non-monotonic term structure. For the proposed market structure, we present a closed form asset pricing model that depends on the factors of the traditional jump-diffusion models, and on both the covariance of the diffusive pricing kernel with price jumps and the covariance of the jumps of the pricing kernel with the diffusive price. We present statistical evidence that these covariances are positive. For our model the expected stock return, jump and diffusive risk premiums are non-linear functions of time.     

A compound option approach to model the interrelation between banking crises and country defaults: The case of Hungary 2008

We analyze the Hungarian financial crisis of 2008 in a stochastic framework that advances structural credit risk models for country defaults: by applying compound option theory we consider payments for bailing-out the banking sector together with debt service payments in a joint crisis model. We estimate the model parameters by applying the time series maximum-likelihood approach of Duan (1994) on yield spreads of Hungarian Bonds. We find that difficulties in acquiring funds for debt servicing in combination with high outstanding debt triggered the crisis, rather than problems in the domestic banking sector. The estimated crisis probabilities dramatically rise during 2008.     

Conditional interest rate risk and the cross‐section of excess stock returns

Differences in excess stock returns can be rationalized by their sensitivities to conditional interest rate risk. Value stocks are particularly sensitive to upside movements in interest rate growth, while growth stocks react strongly to downside movements in interest rate growth. Consistent with the basic asset pricing theory, the upside interest rate risk commands a negative premium which is higher than the premium associated with the downside interest rate risk. Upside beta pertains its explanatory power after controlling for exposure to regular unconditional interest rate and various sources of financial and conditional macroeconomic risk.     

Returns and option activity over the option-expiration week for S&P 100 stocks

For S&P 100 stocks, we find that the weekly returns over option-expiration (OE) weeks (a month’s third-Friday week) tend to be high, relative to: (1) the third-Friday weekly returns of other stocks with less option activity, (2) the own stock’s other weekly returns, (3) the risk, based on asset-pricing alphas. For these same stocks, a month’s fourth-Friday weekly returns underperform modestly. We suggest the following two avenues are likely partial contributors towards understanding these return patterns: (1) delta-hedge rebalancing by option market makers, with a reduction in short-stock hedge positions over the OE week, and (2) declining risk perceptions over the OE week, as measured by option-derived implied volatilities. Our findings suggest option activity can induce reliable patterns in the weekly returns of option-active large-cap stocks.     

American GARCH employee stock option valuation

We implement a flexible simulation-based approach for the fair value of employee stock option (ESO) that accounts for the vesting period, departure risk and voluntary suboptimal early exercise. We introduce GARCH effects on the underlying asset and we analyze the price bias with respect to the constant volatility case. We also perform a sensitivity analysis with respect to changes in several ESO characteristics. We compare this valuation with FAS 123 method revealing a FAS overvaluation. Finally, we value a real ESO plan providing the confidence intervals for the estimated ESO prices.     

VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation

This study integrates CBOE VIX Term Structure and VIX futures to simplify VIX option pricing in multifactor models. Exponential and hump volatility functions with one- to three-factor models of the VIX evolution are used to examine their pricing for VIX options across strikes and maturities. The results show that using exponential volatility functions presents an effective choice as pricing models for VIX calls, whereas hump volatility functions provide efficient out-of-sample valuation for most VIX puts, in particular with deep in-the-money and deep out-of-the-money. Pricing errors for calls can be further reduced with a two-factor model.