Below is MATLAB code to price AMERICAN options using binomial method, can it be modified so it allows for pricing both AMERICAN and EURPEAN options?

function price = binomial_pricer(S0, K, r, sigma, T, type, NumSteps, varargin) % Values American Options, both calls and puts, accommodating different % types of dividends %INPUTS % S0 : Initial Stock Price % K : Strike Price % r : Risk-free Rate % sigma : Stock volatility % T : Term to Maturity % type : Option type = Call 'C' or Put 'P' % NumSteps : Number of steps in binomial tree % varargin : variable number of other input arguments. % No dividend: enter no extra input argument. % Continuous dividend yield % y : - 1 extra input which is the yield. % Discrete dividends % D : the dividend vector % xdate : time to ex-dividend date vector (in years) %OUTPUT % price : option value %% compute tree parameters dt = T/NumSteps; %length of each time step, in years u = exp(sigma*sqrt(dt)); d = 1/u; q = (exp(r *dt) - d)/(u - d); %risk neutral prob of up state df = exp(-r*dt); %discount factor %% Forward propagation to construct the underlying price tree % First, preallocation St = zeros(NumSteps + 1, NumSteps + 1); % matrix to hold underlying prices ft = zeros(NumSteps + 1, NumSteps + 1); % matrix to hold option prices % Construct price tree % Go through different scenarios of dividend based on the number of % variable input arguments n = length(varargin); switch n case 0 % No dividend % Populate the tree with prices St(1,1) = S0; for j = 2:NumSteps + 1 for i = 1:j-1 St(i,j) = St(i, j-1)*u; end St(i+1,j) = St(i, j-1)*d; end case 1 % dividend yield y = varargin{1}; % % Recalculate q q = (exp((r - y)*dt) - d)/(u - d); % Populate the tree with prices St(1,1) = S0; for j = 2:NumSteps + 1 for i = 1:j-1 St(i,j) = St(i, j-1)*u; end St(i+1,j) = St(i, j-1)*d; end case 2 % Scenario 3: discrete dividend % load input variables for this scenario D = varargin{1}; %dividend amount xdate = varargin{2}; %dividend timing % Remove NPV of dividends from initial price pv_D = npv(D, xdate, r); St(1,1) = S0-pv_D; % Construct price tree that excludes the dividend for j = 2:NumSteps + 1 for i = 1:j-1 St(i,j) = St(i, j-1)*u; end St(i+1,j) = St(i, j-1)*d; end % Then add back dividend for nodes that occur before ex div date tau=0; %Track time through tree steps % Iterate through each node of the tree for j = 1:NumSteps % check if current time step is before the dividend div_to_addback = 0; for k=1:length(D) if tau < xdate(k) div_to_addback = div_to_addback + exp(-r*(xdate(k)-tau))*D(k); end end St(:,j)=St(:,j)+ div_to_addback; tau=tau+dt; %Increase by 1 timestep end end %% Compute option prices at terminal nodes and perform backward induction to complete the option price tree if type == 'C' ft(:, end) = max(St(:, end) - K, 0); % Backward induction for j = NumSteps :-1:1 for i = 1:j CV = df * (q*ft(i, j+1) + (1-q)*ft(i+1, j+1)); IV = St(i,j) - K; ft(i,j) = max(CV, IV); end end elseif type == 'P' ft(:, end) = max( K - St(:, end), 0); % Backward induction for j = NumSteps :-1:1 for i = 1:j CV = df * (q*ft(i, j+1) + (1-q)*ft(i+1, j+1)); IV = K - St(i,j); ft(i,j) = max(CV, IV); end end else error('binomial_pricer - Option type must be C or P'); end price = ft(1,1);