Decomposing and valuing callable convertible bonds: a new method based on exotic options

In the framework of Black-Scholes-Merton option pricing models, by employing exotic options instead of plain options or warrants, this paper presents an equivalent decomposition method for usual Callable Convertible Bonds (CCB). Furthermore, the analytic valuation formulae for CCB are worked out by using the analytic formulae for those simpler securities decomposed from CCB. Moreover, this method is validated by comparing with Monte Carlo simulation. Besides, the effects of call clauses, coupon clauses and soft call condition clauses are analyzed respectively. These give lots of new insights into the valuation and analysis of CCB and much help to hedge their risks.Callable convertible bonds; Equivalent decomposition; Up-and-out calls; American binary calls; Derivative pricing

Pricing Moving Window Parisian Option and Applications in Convertible Bonds

AbstractParisian options are complex path-dependent options developed by barrier option. Moving window Parisian options are higher path-dependent options, which are widely used in the field of convertible bonds in recent years. In this work we propose to price moving window Parisian option by use of hitting time. A simulation algorithm of the pricing is presented. As an application, we provide the pricing equations of convertible bonds with reset clause. Furthermore our simulation method is applied to price convertible bonds with reset clause using the data in China mainland stock exchange. The results show that this algorithm can undoubtedly improve the accuracy of the convertible bonds pricing

Obligacje zamienne z klauzulą reset

Obligacja zamienna z klauzulą reset (resettable convertible bond) jest instrumentem, w którymw ściśle określonych terminach oraz w przypadku zaistnienia określonych warunków możliwajest modyfikacja jego istotnych parametrów: ceny konwersji lub współczynnika konwersji. Odróżniają to od zwykłej obligacji zamiennej, w której wszystkie parametry są dokładnie określonew warunkach emisji i nie mogą ulec żadnej zmianie bez względu na uwarunkowania rynkowe.Celem niniejszego opracowania jest przedstawienie istoty reset convertible oraz mechanizmu jejwykorzystania. Potwierdzono hipotezę zakładającą, że jest ona instrumentem bardzo korzystnymdla obligatariuszy w okresie trudnej sytuacji na rynku i spadów cen akcji emitenta. Ponadto okazujesię, że nieznajomość dokładnej wartości współczynnika i ceny konwersji w momencie emisjiobligacji zamiennej z klauzulą reset powoduje trudności z przeprowadzeniem jej precyzyjnejwyceny

Convertible bond pricing: a Monte Carlo approach

Dissertação (mestrado) - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, 2014.Convertible Bonds are interesting hybrid instruments with debt- and equity-like features that have received increasing attention for the last years, especially after the sub-prime mortgage crisis in 2008. This work aims at presenting the main concept behind those instruments, its related features and pricing issues, exhibiting in a constructive manner, from simple products to complex ones, how one may model and price them. To deal with the possibility of American exercises, we implement least-squared and hedged Monte Carlo pricing methods. A clear, flexible, extensible and ready-to-use code implementation for the proposed pricing framework is provided together with some examples of contracts. A discussion of attained numerical results is also presented.Debêntures Conversíveis são interessantes instrumentos híbridos com características de títulos de dívida e de ações que têm recebido atenção crescente nos últimos anos, especialmente após a crise imobiliária americana em 2008. Esse trabalho tem por objetivo apresentar o conceito principal por trás desses instrumentos, suas características e dificuldades de precificação, exibindo de forma construtiva, de produtos simples a outros mais complexos, como alguém consegue modelar e precificá-los. Para lidar com a possibilidade de exercícios Americanos, implementamos os métodos de precificação de Monte Carlo com mínimos quadrados e com cobertura de risco. Uma implementação clara, flexível, extensível e pronta para uso para o framework de precificação proposto é apresentada com alguns exemplos de contratos. Uma discussão de resultados numéricos encontrados também é apresentada

Decomposing and valuing callable convertible bonds: a new method based on exotic options

In the framework of Black-Scholes-Merton option pricing models, by employing exotic options instead of plain options or warrants, this paper presents an equivalent decomposition method for usual Callable Convertible Bonds (CCB). Furthermore, the analytic valuation formulae for CCB are worked out by using the analytic formulae for those simpler securities decomposed from CCB. Moreover, this method is validated by comparing with Monte Carlo simulation. Besides, the effects of call clauses, coupon clauses and soft call condition clauses are analyzed respectively. These give lots of new insights into the valuation and analysis of CCB and much help to hedge their risks

Decomposing and valuing callable convertible bonds: a new method based on exotic options

In the framework of Black-Scholes-Merton option pricing models, by employing exotic options instead of plain options or warrants, this paper presents an equivalent decomposition method for usual Callable Convertible Bonds (CCB). Furthermore, the analytic valuation formulae for CCB are worked out by using the analytic formulae for those simpler securities decomposed from CCB. Moreover, this method is validated by comparing with Monte Carlo simulation. Besides, the effects of call clauses, coupon clauses and soft call condition clauses are analyzed respectively. These give lots of new insights into the valuation and analysis of CCB and much help to hedge their risks

Convertible bond underpricing in the french market : an empirical study

The pricing of convertible bonds is a fairly unstudied field of asset pricing due to the instruments’ complex nature and its niche character. The aim of this dissertation is to compute model implied prices for convertible bonds and compare it to their market value in order to determine whether the market truly underprices convertible bonds, a financial theory that has been discussed broadly in the academic community. As a pricing model I applied a Monte Carlo simulation for stock prices and determined the optimal exercise strategy through the Least-Squares method. With this methodology I priced 34 convertible bonds in the French market and obtained an average underpricing of 4.17%, which reduces to 2.72% when excluding outliers. The results align with previous conducted studies of the French market but are in contrast with some other empirical results in the United States, but due to the substantial difference in convertible bond markets worldwide a direct comparison is not appropriate. Although the finding supports the general claim of convertible bond underpricing and encourages investors to engage in hedging strategies, the lack of substantial research in the European market calls for further empirical studies and improvements of the work presented.A valorização de obrigações convertíveis é um campo muito pouco estudado da valorização de ativos devido à complexidade dos instrumentos e ao seu carácter de nicho. O objetivo desta dissertação é calcular os preços implícitos de obrigações convertíveis e compará-los com o seu valor de mercado a fim de determinar se o seu mercado está realmente subvalorizado, um fenómeno frequentemente descrito por outros autores. Como modelo de preços, apliquei uma simulação Monte-Carlo para os preços das ações e determinei a estratégia ótima de exercício através do método de Least-Squares. Com esta metodologia, fixei o preço de 34 obrigações convertíveis no mercado francês e obtive uma subvalorização média de 4,17%, que reduz para 2,72% ao excluir os outliers. Os resultados estão em linha com estudos anteriores realizados no mercado francês, mas contrastam com outros resultados empíricos nos Estados Unidos; no entanto, devido à diferença substancial nos mercados de obrigações convertíveis em todo o mundo, uma comparação direta não é apropriada. Embora a conclusão apoie a alegação geral de subvalorização de obrigações convertíveis e encoraje os investidores a adotar estratégias de cobertura, a falta de investigação substancial no mercado europeu requer mais estudos empíricos e melhorias do trabalho apresentado

Pricing Convertible Bonds with Credit Risk under Regime Switching and Numerical Solutions

This paper discusses the convertible bonds pricing problem with regime switching and credit risk in the convertible bond market. We derive a Black-Scholes-type partial differential equation of convertible bonds and propose a convertible bond pricing model with boundary conditions. We explore the impact of dilution effect and debt leverage on the value of the convertible bond and also give an adjustment method. Furthermore, we present two numerical solutions for the convertible bond pricing model and prove their consistency. Finally, the pricing results by comparing the finite difference method with the trinomial tree show that the strength of the effect of regime switching on the convertible bond depends on the generator matrix or the regime switching strength