Every node printed, one early exercise found, and the closed form set beside the tree: that sums up the GF561 Unit 4 option valuation walkthrough described below. Searches like "gf 561 unit 4 assignment example", "gf561 unit 4 sample" and "gf561 unit 4 example" land here.
What a finished GF561 Unit 4 option valuation walkthrough looks like
A walkthrough of about six pages built around three trees drawn in full. Inputs sit in a box: share price 48, strike 50, nine months, a 4 percent continuous rate and 32 percent volatility, split into three steps of three months. From those come an up factor of 1.17351, a down factor of 0.85214 and a risk-neutral probability of 0.49136. The share tree runs from 48 to terminal prices of 29.70, 40.90, 56.33 and 77.57. The European call works back to 5.44 and the European put to 5.96. The American put reaches 6.09, because at the lower middle node, a share price of 34.86, exercising returns 15.14 against 14.65 for holding. Black-Scholes then gives 5.06 for the call and 5.58 for the put.
How a GF561 Unit 4 example is structured
Parameters come first, each derived in a line: the step length, the up and down factors from volatility, the growth factor per step and the risk-neutral probability, with a note that this probability is a pricing device rather than a forecast. The share tree follows, then each option tree drawn on the same grid, node values printed above and the discounted expectation shown beside each one. The American tree adds a second number at every node, the exercise value, and circles the node where it wins. A convergence table reports the call at 3, 10, 50 and 200 steps, closing from 5.44 toward 5.06. The Black-Scholes section computes d1, d2 and both normal probabilities, lists the model's assumptions and checks put-call parity for tree and formula alike.
Parameters derived, not quoted
Up and down factors come from 32 percent volatility over three-month steps, and the probability of 0.49136 follows from them and the per-step growth factor.
The share tree on its own
Before any option appears, ten share prices fill the grid, so each payoff at expiry can be read straight off the final column of four.
Backward, one node at a time
Each call value is the probability-weighted average of the two nodes ahead, multiplied by 0.99005 for one step of discounting, and printed where it is computed.
Where holding loses
At 34.86 the American put is worth 15.14 exercised against 14.65 held, and that single node lifts its root value to 6.09 from the European 5.96.
The closed form and what it assumes
Black-Scholes returns 5.06 for the call, and the list beside it names lognormal prices, constant volatility and rates, frictionless continuous trading and exercise only at expiry.
Where marks go in GF561 Unit 4
Lattice work loses most when intermediate values are missing, so a reader sees a final price with no way to locate an arithmetic slip, and partial credit has nowhere to land. A risk-neutral probability computed with the wrong growth factor, annual rather than per step, shifts every node quietly. On American trees, the common failure is comparing exercise and continuation only at expiry, which prices the put as European and misses the 0.13 of early-exercise value. Black-Scholes answers draw deductions when normal probabilities are read at the wrong sign, or when the formula is applied to the American put without comment, since it has no way to value early exercise. Graders also expect a remark on why a three-step tree lands above the formula.
Get a GF561 Unit 4 example written to your instructions
Include the share price, strike, rate, volatility, expiry and step count from the GF561 Unit 4 prompt, plus the rubric, and note whether an American option is required. Each node gets printed and the closed form is checked against the tree. The first custom sample costs nothing, with 24-48h the usual wait.
GF561 Unit 4 questions, answered
How many steps should my tree have?
As many as the prompt specifies, and three is common for hand work because every node stays legible. The sample uses three and then reports the result at 10, 50 and 200 steps from a spreadsheet, showing the value settling near the Black-Scholes figure. That table answers the question graders often ask about accuracy without making the hand-drawn tree unreadable.
Why is the American put worth more than the European one?
Because the holder can exercise before expiry, and in this case doing so beats waiting at one node. Deep in the money, the interest earned on the strike received early outweighs what the option could still gain. The sample shows the exact comparison, 15.14 against 14.65, and the extra 0.13 of value that single decision produces at the root of the tree.
Can Black-Scholes value the American put?
Not directly. The formula assumes exercise only at expiry, so applying it to an American put understates the value whenever early exercise pays. For a call on a share paying no dividends, early exercise is never optimal and the formula still works. The sample states this limit beside the calculation and relies on the lattice for the American figure.