Choosing Volatility Inputs for Options at Different Maturities
Summary
The discussion asks how to price options with several expiration dates when volatility figures are supplied for successive years. The replies distinguish two interpretations: separate vanilla options observed in 2015, or forward volatility periods used to price an option whose future payoff is set later. For separate vanilla options, the suggested approach is to use the volatility associated with each option’s maturity. If the figures represent forward volatilities, the reply describes combining the relevant forward period with earlier volatility to obtain an average volatility over the full maturity.
The answers emphasize that the question’s inputs and payoff timing are ambiguous. For products with multiple future exercise dates, such as a Bermudan option, one response recommends a model that captures volatility dynamics and forward skew, with local volatility as a starting point. The exchange supplies no calculations or pricing results, and the appropriate method depends on what the volatility figures mean and the required accuracy.
Key ideas
- For distinct vanilla options, use the volatility quoted for each option’s maturity.
- Forward volatilities describe volatility over future intervals and must be combined across the option’s full life when pricing from today.
- A Bermudan payoff with multiple future exercise dates calls for a model that represents volatility dynamics and forward skew.
- Local volatility is suggested as a possible starting model, with accuracy needs guiding model choice.
- The question’s interpretation of the volatility quotes remains unclear, so the replies do not give a single definitive pricing recipe.
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Full text
# Value Option with Forward Volatilities # Value Option with Forward Volatilities That is probably a rather simple question but I got confused and would be very thankful for help. Imagine we are in 2015 and have an option that expires in either 2016, 2017, 2018, 2019, 2020 or 2021. We are given the volatilies for t_1 = 31,84%, t_2 = 27,45%, t_3 = 26, 64%, t_4 = 26,27%, t_5 = 26,16% and t_6 = 26,25%. I have to value the option for each expire date and I think I need to use forward volatilities. But can someone tell me what I exactly need to do to price them? What vola do I use for the option that expires in 2016, 2017, ...? Thank you so much! ## Answer by ryc (score 1) https://quant.stackexchange.com/a/55817 If you are referring to an option that is traded in 2015, and its payoff is determined by the spot every year in 2016, 2017, to 2019, e.g. Bermudan payoff - You need a model that can capture the dynamics of volatility, with a reasonable forward skew - Local volatility will be a good start - What model you use depends on what level of accuracy you want to achieve here ## Answer by Oscar (score 1) https://quant.stackexchange.com/a/55818 Your question is very unclear, are these 5 different vanilla options? If so just use the given volatility associated with each of the maturities, t_1, t_2, t_3... to find their prices. Unless you are trying to find the price of an option one year from now, that expires in two years from now I don't see why you would need to use forward volatilities. Or are you perhaps saying that t_2 = 27,45% is the 1-year forward volatility beginning at year 1 (i.e from year 1-2)? If so then you would perhaps use that with the volatility t_1 volatility to find the average yearly volatility for the period year 0-2 in order to value the option with maturity in 2 years from now. Again, I think you need to clarify your question if you want a proper answer.
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