Pricing the European counterpart from American Options
Pricing the European counterpart from American Options
Loading saved threads...
Jared · External communityPost link
External question — Quantitative Finance Stack Exchange
Author: Jared
Original post: https://quant.stackexchange.com/questions/30949
License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/
Adaptation: HTML converted to plain text; contact email addresses removed.
I have American option prices for SPY and need to calculate the equivalent European option price to use in further calculations.
What does it (formally) mean to price the equivalent European option from an American option?
So I have $C_{\text{American}}(K, S, r, T, \delta)$, how do I retrieve $C_{\text{European}}(K, S, r, T, \delta)$?
Edit: are there any methods to price the European put (call) from the market price of the American put (call)?
If the $P_E - P_A \leq 0$ (the American is strictly greater than the European due to exercise premium), will attempts at modeling the time-dependent dividend cash flow provide a model-free approach to price the European counterpart? How do varying interest rates impact these results? Can interest rate variation be safely ignored from some threshold of $T$?
Edit 2: I also can observe the price of the American call. I want to use calls and puts together to strengthen my call
or
put price curve quotes (or other calculations that are derived from them) knowing that OTM options are much more liquid. So even though I cannot trade the ITM call as well, I can get a better idea of its value for modeling purposes from the corresponding put. This is along the same line of thinking because if I could convert to European options I could utilize strict parity, so a method to price the European counterpart would be pricing the source of disparity between the European and the American.
Edit 3: I have found a resource (from 1987) that makes attempts at analytically valuing the difference of an American exercise vanilla vs European exercise:
REFERENCES
Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
Quote
Report
Quantuple · External communityPost link
External answer — Quantitative Finance Stack Exchange
Author: Quantuple
Original post: https://quant.stackexchange.com/a/30951
License: CC BY-SA 3.0 — https://creativecommons.org/licenses/by-sa/3.0/
Adaptation: HTML converted to plain text; contact email addresses removed.
First, you need to specify your working modelling assumptions by selecting a (jump)-diffusion framework, or more exactly, by postulating the risk-neutral dynamics of the underlying (e.g. Black-Scholes).
Then, you choose a pricing method, which should allow you to price both American-style and European-style vanillas (e.g. a binomial lattice)
At this point, using the above pricing method, you should be able to calibrate your model parameters so that they allow you to reproduce the American option price.
Eventually, you can use these calibrated parameters (e.g. the vol, forward and discount actor in BS) to price the European-style counterpart of your American contract.
Quote
Report
Post Reply
Quoted from Forex.com.bd-Editorial External question — Quantitative Finance Stack Exchange Author: Jared Source score (net votes, not local likes): 4 Original post: https://quant.stackexchange.com/questions/30949 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I have American option prices for SPY and need to calculate the equivalent European option price to use in further calculations. What does it (formally) mean to price the equivalent European option from an American option? So I have $C_{\text{American}}(K, S, r, T, \delta)$, how do I retrieve $C_{\text{European}}(K, S, r, T, \delta)$? Edit: are there any methods to price the European put (call) from the market price of the American put (call)? If the $P_E - P_A \leq 0$ (the American is strictly greater than the European due to exercise premium), will attempts at modeling the time-dependent dividend cash flow provide a model-free approach to price the European counterpart? How do varying interest rates impact these results? Can interest rate variation be safely ignored from some threshold of $T$? Edit 2: I also can observe the price of the American call. I want to use calls and puts together to strengthen my call or put price curve quotes (or other calculations that are derived from them) knowing that OTM options are much more liquid. So even though I cannot trade the ITM call as well, I can get a better idea of its value for modeling purposes from the corresponding put. This is along the same line of thinking because if I could convert to European options I could utilize strict parity, so a method to price the European counterpart would be pricing the source of disparity between the European and the American. Edit 3: I have found a resource (from 1987) that makes attempts at analytically valuing the difference of an American exercise vanilla vs European exercise: REFERENCES Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
Checking account access…