Using Black Scholes formula, we know that value of call option is zero when the stock price is zero. We can arrive at the conclusion that the value of option is simply the discounted payoff at expiration. If we assume a lognormal random walk for asset prices, we can arrive at the conclusion that the stock price remains at zero at expiration, and hence the payoff is zero for a call option.Is there any other general intuition behind this? i.e. call option should be zero irrespective of what underlying asset price model we use.

Yes, S=0 must be an absorbing state in any model to avoid an arbitrage opportunity.So, C(S=0)=0 follows.If S=0 is not absorbing, the arbitrage opp is obvious -- simply buy the stock at 0, wait for a positive price, and sell.Another way to say the same thing is that, once your stock is worthless, if you want to return it to play,you (the owner) must recapitalize the company: put in some cash. In reality, the bankruptcy process is, of course, somewhat messier than this, but it certainly doesn't offer a free lunch -- except perhaps to the lawyers.

The same conclusion can be reached from the BS PDE that degenerates to V_t + rV = 0 (1)at S = 0 (Note I use initial condition!)Integrate (1) and use compatibility with the payoff at S = 0 to show that the constant of integration is 0, hece C(S= 0,t) = 0. In this model, the call price will be 0 for any payoff(S) such that payoff(0) = 0.

The equity value can be thought of as a call on the assets of the company, struck at the face value of the liabilities (Merton model). Viewed in this light, so long as the assets are not zero (no matter the level of liabilities), then the equity price can never be zero.

QuoteOriginally posted by: quanuecUsing Black Scholes formula, we know that value of call option is zero when the stock price is zero. We can arrive at the conclusion that the value of option is simply the discounted payoff at expiration. If we assume a lognormal random walk for asset prices, we can arrive at the conclusion that the stock price remains at zero at expiration, and hence the payoff is zero for a call option.Is there any other general intuition behind this? i.e. call option should be zero irrespective of what underlying asset price model we use.Garbage remains garbage

QuoteOriginally posted by: yugmorf2The equity value can be thought of as a call on the assets of the company, struck at the face value of the liabilities (Merton model). Viewed in this light, so long as the assets are not zero (no matter the level of liabilities), then the equity price can never be zero.I do not understand this part "no matter the level of liabilities". E = max(A-L, 0). As long as liabilities are more than asset at liability expiration time, equity will be 0. What am I missing?

optionality

a 0$ asset cannot appreciate. 0 times anyting is zero. If the market deems it worth more than zero, then the call will be priced accordingly, regardless of what formula is used.

QuoteOriginally posted by: quanuecQuoteOriginally posted by: yugmorf2The equity value can be thought of as a call on the assets of the company, struck at the face value of the liabilities (Merton model). Viewed in this light, so long as the assets are not zero (no matter the level of liabilities), then the equity price can never be zero.I do not understand this part "no matter the level of liabilities". E = max(A-L, 0). As long as liabilities are more than asset at liability expiration time, equity will be 0. What am I missing?As Gamel rightly points out, you need to take account of the optionality. Take the example of a large bank that never sleeps - it's possible that such a bank may have had liabilities exceeding assets during the peak of the financial crisis, and yet (because it was a going concern) the equity was still worth something because of the possibility that the assets may appreciate sufficiently so that the company would become solvent at a later date (=optionality).

Good example. During the crisis practically all the big banks had negative capital = assets - liabilities, their stock prices falled down but still remained positive.

QuoteOriginally posted by: yugmorf2QuoteOriginally posted by: quanuecQuoteOriginally posted by: yugmorf2The equity value can be thought of as a call on the assets of the company, struck at the face value of the liabilities (Merton model). Viewed in this light, so long as the assets are not zero (no matter the level of liabilities), then the equity price can never be zero.I do not understand this part "no matter the level of liabilities". E = max(A-L, 0). As long as liabilities are more than asset at liability expiration time, equity will be 0. What am I missing?As Gamel rightly points out, you need to take account of the optionality. Take the example of a large bank that never sleeps - it's possible that such a bank may have had liabilities exceeding assets during the peak of the financial crisis, and yet (because it was a going concern) the equity was still worth something because of the possibility that the assets may appreciate sufficiently so that the company would become solvent at a later date (=optionality).a lot of these big banks also raised fresh equity from investors

use whatever model you would want to value such an option, i would sell you however much you wanted at any number greater than zero...

What about the case where the option is on stock that is not yet issued? For example, I am aware of a situation where the company is going to list in the near future and the executives have options that expire well after the expected listing date, but at this moment the share capital to which the options will relate does not yet exist (authorized, but not issued)I very much doubt that the fair value of the option is zero, but dont have much idea what it would be

I doubt it too, as this example is obviously completely different. What is the value of an IBM call at 3 in the morning?Does a falling tree make a sound in the woods when no one is around to hear it?