It is often argued that the Black Scholes formula is inappropriate in the case where assets are illiquid, or cannot be short sold etc. Is this correct? Consider the following thought experiment.Asset X is illiquid and cannot be short sold, but there are market observable bid offers from which we can agree upon a mid-price reference rate. Suppose a firm sets up two desks, an option desk and a trading desk. In the outside market, the option desk sells a Euro put option on X, struck at K, to pay the difference between K and the reference rate on expiry, if the rate < K.The option desk delta hedges with the trading desk on a contract for difference basis. Trading desk pays a funding charge to option desk, and receives any a 'dividend' payment based on observable dividends for X. I.e. the effect is to replicate the P/L that the trading desk would receive had it actually transacted in the market (except without bid offer or commission slippage). The trading desk is committed to taking any trade from option desk, either bought or sold. All positions unwound on expiry.How do we value the positions held by each desk? I think (1) the option desk position should be valued on a Black Scholes basis, where the drift terms are the expected funding and dividend rates. P/L at maturity for the option desk will reflect its predictions of volatility (and of dividend stream and funding rates). And (2) the expected value of the trading desk (excluding any accumulated or mark to market P/L) will be zero, on the assumption that the value of any risky trading position is zero. Therefore the sum of the two desk valuations will be Black Scholes consistent. Thus, even though the firm as a whole has an unhedged option position, we should value it as if hedged. Is this logic sound?
Last edited by complyorexplain
on May 17th, 2016, 10:00 pm, edited 1 time in total.