An option with a 10 year expiration is close enough to infinite. The further in the future you go the smaller the difference in price.
So do your estimation based upon the curve generated by 3 month, 6 month, and 12 month expirations.
Do you have any idea how much an option with 3 y expiration and the volatility of BTS will cost?
I bet it will be hitting 1usd per 1usd if not more.
I actually think that the option is not infinite in term because the option doesn't have a fixed price. So I think that is the wrong algorithm to use.
When I go short, I am pricing the cost of finding someone else to take over my short position in the future relative to the BitUSD holder wishing to exercise.
With liquidity and no fixed price, the premium can be much lower.
1 bitCNY - is 1) 'smart instrument' and 2)the right to sell this instrument for a price of 1 CNY at any point in the future.
So this is definitely some instrument[we are not concerned with exactly here] plus a put option with strike of 1 CNY [ aka giving you the right to sell said instrument for 1 CNY = straight definition of an option]...except it has no expiration date.
When you are buying the bitCNY you are paying one CNY for the underlying contract (or smart instrument) and anything above 1 CNY is the premium for the put option.
And yes any option definitely has a price (theoretical value) at any point in time.
I think the place you went wrong is saying you have the right to sell said instrument for 1 CNY... which is no true, you have the right to sell it for 1 CNY worth of BTS.
So the person selling the BitCNY into circulation simply has a callable (on-demand) loan. You borrow money that is callable on demand (24 hour notice)... considering the loan is interest-free itself we can consider the premium on BitCNY to be PRICE_OF_OPTION - PREPAID_INTEREST where PREPAID_INTEREST is a variable that represents the value gained by the short and is proportional to the expected change in price of the collateral.
There are a lot of variables in play, but I do not think it is fair to say the premium is just the cost of the option. It factors in the cost of capital for collateral required to stay in the top 98% where you do not have to provide the option.
In other words the bottom 2% of least-collateralized shorts must assume the cost of the option. The other 98% don't have to provide the option. So the premium is pro-rated between these two costs.