How should firms selectively hedge? Resolving the selective hedging puzzle.

We provide a model of intertemporal hedging consistent with selective hedging, a widespread practice corroborated by recent empirical studies. We argue that the optimal hedge is a value hedge involving total current value of future earnings. More importantly, the hedging decision is independent of risk preferences of the firm or agent. Our closed-form solutions imply several implications for the risk management policy in a firm. In order to lock in profits a hedge increase is recommended in favorable states of nature, while in bad states the firm should decrease the hedge and wait. Our main new empirical implication is that selective hedging should be more prevalent in industries where managers are exposed to convex cash flow structures and are more likely to "value hedge" their exposures

Continuous Workout Mortgages

This paper models Continuous Workout Mortgages (CWMs) in an economic environment with refinancings and prepayments by employing a market-observable variable such as the house price index of the pertaining locality. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulae for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable "workout proportion" and adjustable "workout threshold." These results are of importance as they not only help understanding the mechanics of CWMs and estimating key contract parameters. These results are of importance as they not only help in the understanding of the mechanics of CWMs and estimating key contract parameters, but they also provide guidance on how to enhance the resilience of the financial architecture and mitigate systemic risk.Continuous Workout Mortgage (CWM), Repayment, Interest-only, House price index, Prepayment intensity, Cap and floor on continuous flow

Reducing the impact of real estate foreclosures with Amortizing Participation Mortgages

We employ Amortizing Participation Mortgage (APM) to offer a novel ex post renegotiation method of a foreclosure. APM belongs to the family of home loan credit facilities advocated in the Dodd-Frank Wall Street Reform and Consumer Protection Act 2010. In our framework, APMs reduce the endemic agency costs of debt by improving affordability. These benefits increase the demand for real estate in bust times and reduce fragility of the financial system thereby preventing foreclosures. We evaluate APMs in a stochastic control framework and provide solutions for an optimal amortization schedule. We generalize our approach to partially amortizing and commercial mortgages which encompass balloon payments. Finally, we provide concrete numerical examples of home loan modifications. We also offer detailed sensitivity analysis to market parameters such as house price volatility and interest rates

Continuous Workout Mortgages

This paper models Continuous Workout Mortgages (CWMs) in an economic environment with refinancings and prepayments by employing a market-observable variable such as the house price index of the pertaining locality. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulae for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable “workout proportion” and adjustable “workout threshold.” These results are of importance as they not only help understanding the mechanics of CWMs and estimating key contract parameters. These results are of importance as they not only help in the understanding of the mechanics of CWMs and estimating key contract parameters, but they also provide guidance on how to enhance the resilience of the financial architecture and mitigate systemic risk

Continuous Workout Mortgages

Continuous Workout Mortgage (CWM) balance and payments are indexed using market-observable house price index in an economic environment with prepayments. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulas for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable "workout proportion" and adjustable "workout threshold." These results are of importance as they not only help in the understanding of the mechanics of CWMs and estimating key contract parameters, but they also provide guidance on how to enhance the resilience of the financial architecture and mitigate systemic risk.

Continuous Workout Mortgages:Efficient Pricing and Systemic Implications

This paper studies the Continuous Workout Mortgage (CWM), a two in one product: a fixed rate home loan coupled with negative equity insurance, to advocate its viability in mitigating financial fragility. In order to tackle the many issues that CWMs embrace, we perform a range of tasks. We optimally price CWMs and take a systemic market-based approach, stipulating that mortgage values and payments should be linked to housing prices and adjusted downward to prevent negative equity. We illustrate that amortizing CWMs can be the efficient home financing choice for many households. We price CWMs as American option style, defaulting debt in conjunction with prepayment within a continuous time, analytic framework. We introduce random prepayments via the intensity approach of We also model the optimal embedded option to default whose exercise is motivated by decreasing random house prices. We adapt the (BAW) approach to work within amortizing mortgage context. We derive new closed-form and new analytical approximation methodologies which apply both for pricing CWMs, as well as for pricing the standard US 30-year Fixed Rate Mortgage (FRM)

Couverture dynamique optimale du risque de change de long terme pour une entreprise

Chapter 1 : Optimal dynamic level risk hedging for a corporation. An optimal hedging of the exchange rate risk for a firm is considered. The concept of the long term exchange rate risk is defined by opposition to the classic exchange rate risk. The optimal hedge of the intertemporal long term exchange rate risk is derived by the method of stochastic optimal control, in a model where the exchange rate follows a Gaussian process with return to the level of parity. It is demonstrated that such a hedge is a hedge in value, that stabilizes the dividends flow paid to shareholders and depends on the level of the exchange rate with respect to the level parity. The model is rich in practical recommendation for risk management policy in a firm. It appears that the corporation would have to hedge more if the level of the exchange rate is above the level of parity -so as to freeze profits- and to adopt an inverse behavior in the opposite case. Chapter 2 : Optimal dynamic level risk hedging for a corporation in incomplete market. We solve an incomplete markets hedging problem for a corporation exposed to a long term risk of revenue level and endowed with non-exchangeable assets. The incompleteness is generated in the model by a multiplicative and non-hedgeable risky component assimilated to the size of the cash-flow coming from abroad. The optimal policy is obtained by the method of fictitious completion. It is demonstrated that the incompleteness reduces considerably the size of the hedge, as compared to that observed in complete markets. Chapter 3 : Hedging, information arrival & investment. This article approaches aspects concerning the optimal hedging and investment decision making in a corporation. It is shown that depending on the information arrival timing and costs of external financing the optimal risk management position on the forward market varies from true hedging to pure speculation. The presence of non-tradable assets seems to be crucial.Cette thèse se compose de trois articles: 1. Couverture du risque de change en marché complet. Cet article concerne la couverture optimale du risque de change pour une entreprise. Le concept du risque de change de long terme est défini par opposition à la conception classique du risque de change. La couverture optimale intertemporelle du risque de change de long terme est ensuite dérivée par la méthode de contrôle optimal stochastique, dans le cadre d'un modèle où le taux de change suit un processus gaussien avec retour vers le niveau de parité. Il est démontré qu'une telle couverture est une couverture en valeur, qui stabilise le flux des dividendes payés aux actionnaires et dépend du niveau du taux de change par rapport au taux de parité. Le modèle développé dans cet article est riche en recommandations pratiques pour la politique de gestion des risques dans une entreprise. Il apparaît notamment que l'entreprise devrait se couvrir plus si le niveau du taux de change est au-dessus du niveau de parité afin de geler les profits et adopter un comportement inverse dans le cas contraire. 2. Couverture du risque de change en marché incomplet Cet article concerne le problème de couverture du risque de change de long terme en présence des actifs non-échangeables dans le contexte des marchés incomplets. L'incomplétude est générée dans le modèle par un risque multiplicatif et non-couvrable de taille du flux provenant du pays étranger. La couverture optimale est obtenue par la méthode de fictitious completion. Il est démontré que l'incomplétude réduit considérablement la taille de couverture, par rapport à celle observée en marché complet. 3. Couverture du risque de change et décision d'investissement Cet article aborde les aspects concernant l'arrivée de l'information et la prise de décision de couverture optimale du risque de change et celle d'investissement pour une entreprise en présence des actifs non échangeables et coûts de financement externes

On the Equivalence of Floating and Fixed-Strike Asian Options

There are two types of Asian options in the financial markets which differ according to the role of the average price. We give a symmetry result between the floating and fixed-strike Asian options. The proof involves a change of numeraire and time reversal of the Brownian motion. Symmetries are very useful in option valuation and in this case, the result allows the use of more established fixed-strike pricing methods to price floating-strike Asian options.