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The Options Based Portfolio Insurance (OBPI) should avoid losses and capture gains, by the cost of a “premium”, but in practice the premium cost can be too high to capture gains in the different market conditions. Based on this premise, the objective of this study is to analyze an optimized alternative to Options Based Portfolio Insurance, assuming that the probability of an Extreme Negative Event varies with time, and therefore the insurance floor should not be maintained at any cost. To achieve the objective, data were crossed between the rollover date and a fixed insurance cost on equity, using historical data from 678,546 trades carried out in the US market, which resulted in 3,700 portfolios. Data analysis was performed using descriptive and econometric statistics with simple linear regressions. The results demonstrated that the insured floor varied with the volatility implied in option prices, indicating the possibility of obtaining better return-risk ratio and lower drawdown when compared to the unprotected portfolio, showing a positive correlation between insurance cost and return-risk ratio for low costs and a negative correlation for higher costs. Furthermore, it can be indirectly inferred that the explanation for the results comes from the perception of risk by the market not representing the real risk. As with the stabilization and possible recovery of prices that occur after a significant drop, market confidence is not restored to the same proportion. That’s why volatility remains at high levels, consequently, raising the insurance cost, even with lower probabilities of Extreme Negative Events.     

The aim of this paper is to evaluate barrier options by considering volatility as stochastic following the CIR process used in Heston (1993). To solve this problem, we used Monte Carlo simulation. We studied the effects of stochastic volatility on the value of the barrier option by considering different values of the determinants of the option. We illustrated these effects in twelve graphs. We found that in general, regardless of the parameter under study, the stochastic volatility model significantly overvalues the in-the-money (ITM) barrier options, and slightly the deep-in-the money (DIP) options, while slightly undervaluing the near-out-the money (NTM) options.

The purpose of this study is to investigate the suitable arbitrage-free term-structure model that might be able to fit the South African inflation-indexed spot-rate curve. The instrument has relatively less tradability in the market, which then translates into a lack of adequate data for bond valuation/pricing. Pricing deviations might give inflated/deflated projections on the value of government debt; consequently, higher estimated interest cost to be paid. A proper valuation of these instruments is mandatory as they form part of government funding/borrowing and the country’s budgeting processes in the medium term. The performance of newly developed non-linear multifactor models that follows the Nelson-Siegel (1987) framework was compared to the arbitrage-free Vasicek (1977) model and linear parametric models to assess any significant deviations in forecasting the real spot-rate curve over a short period. Models with constant parameters (i.e. linear parametric, cubic splines, Nelson-Siegel (1987) and Svensson (1994)) gave a perfect fit, they proved to marginally lose fitting capabilities during periods of higher volatility. Therefore, it could be concluded that the application of either Nelson-Siegel (1987) model or Svensson (1994) model on forecasting South African real spot-rate curve gave a perfect fit. However, for a solid conclusion to be derived, it is imperative to explore the performance of these models over a period of stressed market and economic conditions.

In this study, the option pricing performance of the adjusted Black-Scholes model proposed by Corrado and Su (1996) and corrected by Brown and Robinson (2002), is investigated and compared with original Black Scholes pricing model for the Turkish derivatives market. The data consist of the European options written on BIST 30 index extends from January 02, 2015 to April 24, 2015 for given exercise prices with maturity April 30, 2015. In this period, the strike prices are ranging from 86 to 124. To compare the models, the implied parameters are derived by minimizing the sum of squared deviations between the observed and theoretical option prices. The implied distribution of BIST 30 index does not significantly deviate from normal distribution. In addition, pricing performance of Black Scholes model performs better in most of the time. Black Scholes pricing Formula, Carrado-Su pricing Formula, Implied Parameters