I have this answer from book which i don't understand how to find the circle number. I dont see any calculations. please help me.

or p=0.7564. The value of the option is then its expected payoff discounted at the risk. free rate: [00.7564+50.2436e0.10.5=1.16 or $1.16. This agrees with the previous calculation. 12.5 In this case, u=1.10,d=0.90,t=0.5, and r=0.08, so that p=1.100.90e0.080.50.90=0.7041 The tree for stock price movements is shown in the following diagram. We can work back from the end of the tree to the beginning, as indicated in the diagram. to give the value of the option as $9.61. The option value can also be calculated directly from equation (12.10): [0.7041221+20.70410.29590+0.295920]e20.080.5=9.61 or $9.61. 6 The diagram overleaf shows how we can value the put option using the same tree as in Quiz 12.5. The value of the option is \$1.92. The option value can also be calculated Imroduction to Binomial Trees 309 12.2. Explain the no-arbitrage and risk-neutral valuation approaches to valuing a European option using a one-step binomial tree. 12.3. What is meant by the delta of a stock option? 12.4. A stock price is currently $50. It is known that at the end of six months it will be either $45 or $55. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a six-month European put option with a strike price of $50 ? 12.5. A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100 ? 12.6. For the situation considered in Problem 12.5, what is the value of a one-year European put option with a strike price of $100 ? Verify that the European call and European put prices satisfy put-call parity. 12.7. What are the formulas for u and d in terms of volatility