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Abstract:
In this paper we propose a simple and easy-to-use method for computing accurate estimate (in closed form) of the double barrier hitting time distribution of a mean-reverting lognormal process, and discuss its application to pricing exotic options whose payoffs are contingent upon barrier hitting times. This new approach is also able to provide tight upper and lower bounds (in closed form) of the exact result. Within the multi-stage approximation scheme, the estimate and bounds can be easily improved in a systematic manner. Furthermore, this approach can be straight-forwardly extended to those cases with specified moving boundaries as well.

First hitting time, mean-reverting lognormal process, barrier options, method of images

Abstract:
Given the deleveraging process in the banking sector, banks were reluctant to lend funds in the inter-bank market because of uncertainty about their own future need for funds during the financial crisis of 2007-2009. Aggregate liquidity then declined. This paper investigates the impact of the market-wide liquidity risk and carry-trade incentives on exchange rate movements. The results suggest that liquidity risk measured by the spread between Libor and the overnight index swap rate was a significant factor affecting the exchange rate movements of the euro, the British pound and the Swiss franc, while carry trades were important for the yen, the Australia dollar and the New Zealand dollar.

Sub-prime crisis, carry trades, liquidity, leverage

Abstract:
This paper proposes a path-dependent approach for estimating maximum appreciations of the renminbi expected by the market based on first-passage-time distributions. Using market data of the renminbi spot exchange rates, non-deliverable forward rates and currency option prices from 21 July 2005 (the reform of the exchange rate regime) to 28 February 2008 for model parameters, the maximum appreciations of the renminbi estimated under the proposed approach show that the market expected another large movement of the exchange rate during the 14 months after the reform. Subsequently, the few occasions of appreciations beyond the expected maximums coincided with the trade-related issues and speculations of greater momentum of appreciation allowed by the authorities. The PBoC's measures were however largely incorporated into the derivatives' prices. The proposed approach can be used to gauge the range of appreciations of the renminbi anticipated in the market and to identify any exchange rate movements beyond market expectations.

renminbi exchange rate, first-passage-time distributions, currency options

Abstract:
This paper proposes a path-dependent approach for estimating maximum appreciations of the renminbi expected by the market based on first-passage-time distributions. Using market data of the renminbi spot exchange rates, non-deliverable forward rates and currency option prices from 21 July 2005 (the reform of the exchange rate regime) to 28 February 2008 for model parameters, the maximum appreciations of the renminbi estimated under the proposed approach show that the market expected another large movement of the exchange rate during the 14 months after the reform. Subsequently, the few occasions of appreciations beyond the expected maximums coincided with trade-related issues and speculation that greater momentum of appreciation would be allowed by the authorities. The PBoC's measures were however largely incorporated into the derivatives' prices. The proposed approach can be used to gauge the range of appreciations of the renminbi anticipated in the market and to identify any exchange rate movements beyond market expectations.

renminbi exchange rate, first-passage-time distributions, currency options

Abstract:
This note analyses the impact of the global credit crisis on the FX swap market and discusses its potential implications. The turbulence in money markets has spilled over to FX swap markets amid a reappraisal of counterparty risks during the recent financial turmoil. We examine the situations of six currencies including the euro, the British pound, the Australian dollar, the Japanese yen, the Hong Kong dollar and the Singapore dollar. We find that (i) the risk premiums have indeed gone in tandem with the spreads of money market rates over their corresponding overnight index swaps across the economies, a popular measure of potential banking insolvency; and (ii) the risk premiums bear a negative relationship with the strength of the spot rates of the respective currencies, which is consistent with the increased pressure in the swap markets.

FX swaps, covered interest parity, counterparty risk

Abstract:
Significant deviations from covered interest parity were observed during the financial crisis of 2007-2009. This paper finds that before the failure of Lehman Brothers the market-wide funding liquidity risk was the main determinant of these deviations in terms of the premiums on swap-implied US dollar interest rates for the euro, British pound, Hong Kong dollar, Japanese yen, Singapore dollar and Swiss Franc. This evidence suggests that the deviations can be explained by the existence and nature of liquidity constraints. After the Lehman default, both counterparty risk and funding liquidity risk in the European economies were the significant determinants of the positive deviations, while the tightened liquidity condition in the US dollar was the main driving factor of the negative deviations in the Hong Kong, Japan and Singapore markets. Federal Reserve Swap lines with other central banks that eased the liquidity pressure reduced the positive deviations in the European economies.

sub-prime crisis, funding liquidity, covered interest parity, FX swaps

Abstract:
This paper proposes a path-dependent approach for estimating realignment probabilities of targeted exchange rates based on the first-passage-time (FPT) density instead of the commonly used path-independent approach. We consider that path dependency is an intrinsic characteristic of realignment risk because a realignment of an exchange rate can occur whenever a committed band by a central bank is breached. A mean-reverting lognormal process is considered in the FPT approach. Based on market data of the British pound and Italian lira during the ERM crisis of 1992, the realignment probabilities of the currencies estimated under the proposed approach show that path dependency is quantitatively significant, compared with the path-independent approach. The first-hitting time and the time of the maximum slope of the FPT density have forward-looking capability of assessing realignment risk of the pound and lira target zones.

realignment risk, ERM crisis, first-passage-time probability

Abstract:
This paper examines pricing anomalies in the interest rate markets during the financial crisis of 2007-2009. Before the failure of Lehman credit and funding constraints weakened the relationship between interest rates of LIBOR and derivatives in the euro, British pound and US dollar, with equivalent discounted cash flows, and hence gave rise to pricing anomalies that would not usually exist. After the Lehman failure, the pricing anomalies in the two European currencies reduced with the relaxation of the funding constraint. The funding and credit constraints however became insignificant for the pricing anomalies in the dollar which persisted during the first half of 2009.

Interest rate markets, sub-prime crisis, funding constraints, pricing anomalies