The Black Scholes Option Pricing Theory - 2335 Words

Client Specification My uncle in law is Portuguese who has been living in Macao for more than 20 years. Recently he plans to go back to Portugal after his retirement. Portugal has been in deep recession for 5 years and is the third European country to need a bail out. After noticing the default crisis in Greece and Argentina, he is worried about Portugal will default very soon under the impact of European sovereign credit crisis. Therefore I want to use my knowledge gained in this year to solve his puzzle. Regarding that my uncle in law does not have strong econometric knowledge, simple method with detailed steps and theory is preferred. This report aims to use the basic Merton Model with brief described procedure to compute sovereign†¦show more content†¦In order to calculate the sovereign probability of default, Gray et al (2007) suggests a sovereign capital structure which simply use the information from the sovereign balance sheet and apply the Merton Model for the estimation of sovereign asset and volatility. It has been proved by Sy-Hoa Ho (2014) with the evidence from Argentina and initially mentioned in Van et al (2005) with the Netherlands case. In Figure 1, the 5-YR CDS shows high bp starting from late-2009 to late-2012 and a gradually decreasing trend starting from the late-2013. In Figure 2, it is observed that there is steady and significant increase in the percentage debt of total GDP in Portugal since 2009 compared with others. Besides, there is a slowdown of the increasing trend in the last two years. Specification Sovereign Asset Sovereign assets is a state owned asset and is equal to the sum of the sovereign equity and sovereign debt at any time. V_t=S_t+B_t (1) According to Gray et al (2007, Page 10), it states that â€Å"sovereign assets includes the foreign currency reserves (R_MA), public asset (A_Other) and net fiscal asset (A_G) which is the present value of taxes and revenues â€Å"and is expressed in the following equation: A_S=R_MA+A_G+A_Other=M_BM+(B Ì…_SLC-P_SLC )+(B Ì…_SFX-P_SFX )+ÃŽ ±P_F where M_BM-monetary base (B Ì…_SLC-P_SLC ) is the risky debt of local (domestic) currency (B Ì…_SFX-P_SFX ) is the risky debt of foreign