مهندسی مالی

شرح پروژه

One method for calculating the price of volatility risk is to synthesise a log contract from a portfolio of options. Your task is to create a portfolio of liquid options that mimics the payoff of a log contract according to the formula ∗

􏰀𝐾􏰁􏰂􏰃𝑆􏰄􏰅𝐾􏰆􏰇Δ𝐾􏰊􏰀𝐾􏰁􏰂􏰃𝐾􏰅𝑆􏰄􏰆􏰇Δ𝐾􏰌𝑆􏰄􏰅𝐾 􏰊ln𝐾∗􏰅ln𝑆􏰄, 􏰃𝟏􏰆 􏰈􏰉􏰈∗ 􏰈􏰋􏰈∗ 𝐾∗

where 𝐾 are strike prices with spacing Δ𝐾 and 𝐾∗ is a threshold that separates liquid call options from liquid put options.

The enclosed spreadsheet contains European call and put option prices on Euro Stoxx 50 index as of 15-01-2019, for a range of strikes and a single expiration date 𝑇 of 21-06-2019. Use this data to

1. Decide on the appropriate value of 𝐾∗;

2. Decidewhatstrikerangetoincludeinyoursyntheticportfolio,considering

   the liquidity of the available options;

3. Computethevalueofthesyntheticportfolioasof15-01-2019;

4. Compute the value of Black–Scholes volatility compatible with the price of

   the synthetic portfolio;

5. Comment on the size of volatility premium implied by your calculation, given

   that historical volatility of the index on 15-01-2019 was estimated to be

   10.5%;

6. Discuss how the limited number of strike values in your synthetic portfolio

   impacts on the precision of the approximation in equation (1);

7. Collect your own data and rerun the same type of analysis for a different

   start date/ different expiration date and/or different underlying index.

این پروژه شامل 1 فایل مهم است، لطفا قبل از ارسال پیشنهاد حتما نسبت به بررسی این فایل اقدام فرمایید.

مهارت ها و تخصص های مورد نیاز

درباره کارفرما

کاربر165693

عضویت چهار سال پیش

2 پروژه ثبت شده ،

0 پروژه در حال انجام ،

0 پروژه آماده دریافت پیشنهاد ،

نرخ پذیرش پیشنهاد 50%