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4

Note that \begin{align*} (K-S_T)^+ \ge K-S_T. \end{align*} Then \begin{align*} p &\equiv E\Big(e^{-rT} (K-S_T)^+ \Big)\\ &\ge E\Big(e^{-rT} (K-S_T) \Big)\\ &=K\, e^{-rT} - S_0\\ &= 670 \times e^{-0.05 \times 55/365} - 563.48\\ &=102.49. \end{align*} However, the option price is 101.375, which is smaller. This is the reason that you have ...


3

A possible reason may be your computation of maturity period. Exchange compute the maturity in minute till expiry and then divide it by total trading minute in a year to arrive at maturity. An another possible reason may be your choice of risk free interest rate. There are various proxy for risk free interest rate like Treasury rate and LIBOR of different ...


2

The simple answer is no. You need historical data to backuo the implied correlation. A smart way to do it is to use Buss and Vilkov (2009) methodology. Denote the risk-neutral correlation between each pair of stocks: $\rho_{ij,t}^Q$. The presence of the correlation premia led Buss and Vilkov (2009) to estimate the risk-neutral correlation by making: ...


2

You can guesstimate by vega weighted implied vol. This is why: Say that you have a portfolio of options with prices $P_j$. Each one of them has a different pricing function $f_j$ (as function of vol) and a different implied vol $\sigma_j$. For each option $f_j(\sigma_j)=P_j$. Now you put them together in a single product. If the implied vol of the product ...


1

They expire 30 days before the expiration of the S&P monthly options. The latter usually expire on the third Friday of the month (however, in rare cases the S&P opts. expire on Thursday because the Friday is a holiday; the last time it happened was April 17, 2014 since April 18 2014 was a NYSE holiday). Neglecting the holiday thing, the expiration ...


1

Probably because volib assumes that the Black-Scholes holds which as we not is not true. A better way to compute implied volatility is to use a Moment-Free-Implied-Measure. One possibility is to closely following the model-free estimate proposed by Demeter et al. (1999) and Carr and Madan (1998) who show that if one owns a portfolio of options across all ...



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