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the call version pays $$ I_{S_T > K } S_T $$ the put version pays $$ -I_{S_T < K } S_T $$ Subtract to get a pay-off $$ S_T. $$ (ignoring the probability zero event of $S_T=K.$) So the prices subtract to give $S_0.$


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Sorry to disagree but if interest rates is 0, the binary is still not worth $1 now. Suppose spot $S(0) = 100$, assume $x = 110$ and upon touch (whenever it happens as the option has no maturity) you receive one dollar. Suppose I buy 1 stock. If the barrier hits, i sell the stock and receive 110 USD. What if I buy N stocks at t=0? upon hit of barrier i ...


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there are has been a lot of papers on the analysis of the convergence of binomial trees for European options. You can regard a tree as an explicit finite difference method. The conclusions are that the location of the nodes near the strike determine the error. So if $\kappa$ is the fraction of the distance between the strike and the lower node as opposed to ...


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What the author is arguing is that the current price exactly at this instant takes into account all the views of the market participants as expressed by orders (which would be correct). Note that those views may change almost instantaneously generating orders thus causing price to change. An example is you have an expected future price of 10 and the current ...


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Mark has rightly pointed. You may think like this, If there is high probability price would go up in future(in very short period), lets say 90% then investors would continue to buy until they no longer expect price to increase with such a high probability. Or until this strategy of buying shares with high probability of going up is not profitable(excess ...


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well, the current share price reflects fair value. So you'd expect it to be close to its expected price, but slightly below because of risk aversion and discounting. If it was very far off its expectation, it would either be over or under valued and people would trade accordingly.


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Rather than thinking about the steps, think about the piecewise regions where your value is constant. When using the explicit scheme, time zero option value at any stock price for your simple digital option is basically just a function of which antecedent nodes (accounting for backwards timestepping) were above or below the strike. Slight modifications of ...



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